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Groups > comp.lang.c++ > #118554 > unrolled thread
| Started by | wij <wyniijj5@gmail.com> |
|---|---|
| First post | 2024-03-26 22:51 +0800 |
| Last post | 2024-03-29 05:06 +0800 |
| Articles | 20 on this page of 55 — 11 participants |
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Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-26 22:51 +0800
Re: Repeating decimals are irrational Michael S <already5chosen@yahoo.com> - 2024-03-26 17:11 +0200
Re: Repeating decimals are irrational Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-03-26 16:13 +0000
Re: Repeating decimals are irrational Marcel Mueller <news.5.maazl@spamgourmet.org> - 2024-03-27 21:34 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:13 -0700
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 05:43 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 12:50 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 20:12 +0800
Re: Repeating decimals are irrational Ralf Goertz <me@myprovider.invalid> - 2024-03-27 13:57 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 21:32 +0800
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-27 21:49 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 16:01 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:34 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 16:02 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-28 00:05 +0800
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:40 -0700
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-28 05:39 +0800
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 15:10 -0700
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 15:14 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:17 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 02:25 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 11:36 +0100
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:16 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 02:23 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 11:53 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 23:14 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 16:48 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-30 00:16 +0800
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:43 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 15:44 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:40 -0700
Re: Repeating decimals are irrational Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-29 11:35 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 15:49 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-30 23:14 +0800
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-30 19:26 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-31 03:30 +0800
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:29 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 15:51 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 21:52 -0700
Re: Repeating decimals are irrational Paavo Helde <eesnimi@osa.pri.ee> - 2024-03-26 23:51 +0200
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 19:42 -0700
Re: Repeating decimals are irrational Paavo Helde <eesnimi@osa.pri.ee> - 2024-03-27 11:47 +0200
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 13:10 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:45 -0700
Re: Repeating decimals are irrational Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-04-25 16:33 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-04-26 12:46 +0200
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-27 11:31 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:17 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-28 18:47 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 12:41 -0700
Re: Repeating decimals are irrational David Brown <david.brown@hesbynett.no> - 2024-03-29 13:03 +0100
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:33 -0700
Re: Repeating decimals are irrational "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 19:20 -0700
Re: Repeating decimals are irrational usenet@stegropa.de (Stefan Große Pawig) - 2024-03-28 21:33 +0100
Re: Repeating decimals are irrational wij <wyniijj5@gmail.com> - 2024-03-29 05:06 +0800
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-29 02:25 +0800 |
| Message-ID | <23af13dd2b0281969a874a2913983c0621de68bd.camel@gmail.com> |
| In reply to | #118608 |
On Thu, 2024-03-28 at 18:17 +0100, David Brown wrote: > On 27/03/2024 22:39, wij wrote: > > On Wed, 2024-03-27 at 13:40 -0700, Chris M. Thomasson wrote: > > > On 3/27/2024 9:05 AM, wij wrote: > > > > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: > > > > > On 27/03/2024 14:32, wij wrote: > > > > > > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: > > > > > > > Am Wed, 27 Mar 2024 20:12:38 +0800 > > > > > > > schrieb wij <wyniijj5@gmail.com>: > > > > > > > > > > > > > > > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: > > > > > > > > > On 26/03/2024 22:43, wij wrote: > > > > > > > > > > > > > > > > > > > > Just repeat the pattern infinitely, then it is irrational. > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) > > > > > > > > > > cannot terminate, 1/7 != 0.(142857) > > > > > > > > > > > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > > > > > > > I am surprise your math. knowledge is so low worse than teenagers. > > > > > > > > > > > > > > Use the standard trick: > > > > > > > > > > > > > > x=0.[142857] => 1,000,000*x=142857.[142857] > > > > > > > > > > > > > > subtract the first equation from the second: > > > > > > > > > > > > > > 999,999*x=142857 => x=142857/999,999=1/7 > > > > > > > > > > > > > > > > > > > To determine whether a number x is rational or not, we can repeatedly subtract > > > > > > rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite > > > > > > steps, then x is rational. Otherwise, x is irrational. > > > > > > If x is a repeating decimal, proposition "repeating decimal is rational" is > > > > > > simply false by sematics. > > > > > > > > > > > > > > > > Let me just ask you two simple questions: > > > > > > > > > > Do you think 1/7 is a rational number or an irrational number? > > > > > > > > > rational > > > > > > > > > What do you think the decimal expansion of 1/7 is? > > > > > > > > > > > > > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure > > > > never terminates which means the conversion is never complete. > > > > > > > > > > > > > > > > > > You can stop iteration as soon as you detect a cycle, or period if you > > > will. In 1/7, say it took 6 iterations to hit the period... Sound okay? > > > > Stupid! It is an infinite string. Cycle or period can only be determined for > > finite string. > > > > Nonsense. > > You /know/ the cycle for the infinite decimal expansion for 1/7 - it is > the digits "142857", repeated every 6 digits in the decimal expansion. > Again, that's what the notation 0.(142857) - /your/ choice of notation, > so presumably familiar to you - means. > "0.(142857)" is pre-determined and specified not detected. (unless I misunderstood what Chris said)
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-29 11:36 +0100 |
| Message-ID | <uu65jl$8106$1@dont-email.me> |
| In reply to | #118611 |
On 28/03/2024 19:25, wij wrote: > On Thu, 2024-03-28 at 18:17 +0100, David Brown wrote: >> On 27/03/2024 22:39, wij wrote: >>> On Wed, 2024-03-27 at 13:40 -0700, Chris M. Thomasson wrote: >>>> On 3/27/2024 9:05 AM, wij wrote: >>>>> On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: >>>>>> On 27/03/2024 14:32, wij wrote: >>>>>>> On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >>>>>>>> Am Wed, 27 Mar 2024 20:12:38 +0800 >>>>>>>> schrieb wij <wyniijj5@gmail.com>: >>>>>>>> >>>>>>>>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>>>>>>>> On 26/03/2024 22:43, wij wrote: >>>>>>>>>>> >>>>>>>>>>> Just repeat the pattern infinitely, then it is irrational. >>>>>>>>>> >>>>>>>>>> Nonsense. >>>>>>>>>> >>>>>>>>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>>>>>>>> cannot terminate, 1/7 != 0.(142857) >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Nonsense. >>>>>>>>>> >>>>>>>>> >>>>>>>>> I am surprise your math. knowledge is so low worse than teenagers. >>>>>>>> >>>>>>>> Use the standard trick: >>>>>>>> >>>>>>>> x=0.[142857] => 1,000,000*x=142857.[142857] >>>>>>>> >>>>>>>> subtract the first equation from the second: >>>>>>>> >>>>>>>> 999,999*x=142857 => x=142857/999,999=1/7 >>>>>>>> >>>>>>> >>>>>>> To determine whether a number x is rational or not, we can repeatedly subtract >>>>>>> rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite >>>>>>> steps, then x is rational. Otherwise, x is irrational. >>>>>>> If x is a repeating decimal, proposition "repeating decimal is rational" is >>>>>>> simply false by sematics. >>>>>>> >>>>>> >>>>>> Let me just ask you two simple questions: >>>>>> >>>>>> Do you think 1/7 is a rational number or an irrational number? >>>>>> >>>>> rational >>>>> >>>>>> What do you think the decimal expansion of 1/7 is? >>>>>> >>>>> >>>>> When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure >>>>> never terminates which means the conversion is never complete. >>>>> >>>>> >>>>> >>>> >>>> You can stop iteration as soon as you detect a cycle, or period if you >>>> will. In 1/7, say it took 6 iterations to hit the period... Sound okay? >>> >>> Stupid! It is an infinite string. Cycle or period can only be determined for >>> finite string. >>> >> >> Nonsense. >> >> You /know/ the cycle for the infinite decimal expansion for 1/7 - it is >> the digits "142857", repeated every 6 digits in the decimal expansion. >> Again, that's what the notation 0.(142857) - /your/ choice of notation, >> so presumably familiar to you - means. >> > "0.(142857)" is pre-determined and specified not detected. (unless I misunderstood > what Chris said) > You are so confused that I would not be surprised if you misunderstood Chris. And Chris' posts score much higher on enthusiasm than on clarity. The fact that 1/7 has the decimal expansion 0.(142857) - that is, an unending repetition of the digits 142857 - is simple to calculate and easy to prove correct. It is "pre-determined" in the sense that it is the unique decimal expansion for 1/7. But I don't understand what you mean by "specified and not detected" - it is not something that Chris invented out of thin air.
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-28 18:16 +0100 |
| Message-ID | <uu48kk$3n14g$1@dont-email.me> |
| In reply to | #118580 |
On 27/03/2024 17:05, wij wrote: > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: >> On 27/03/2024 14:32, wij wrote: >>> On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >>>> Am Wed, 27 Mar 2024 20:12:38 +0800 >>>> schrieb wij <wyniijj5@gmail.com>: >>>> >>>>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>>>> On 26/03/2024 22:43, wij wrote: >>>>>>> >>>>>>> Just repeat the pattern infinitely, then it is irrational. >>>>>> >>>>>> Nonsense. >>>>>> >>>>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>>>> cannot terminate, 1/7 != 0.(142857) >>>>>>> >>>>>> >>>>>> Nonsense. >>>>>> >>>>> >>>>> I am surprise your math. knowledge is so low worse than teenagers. >>>> >>>> Use the standard trick: >>>> >>>> x=0.[142857] => 1,000,000*x=142857.[142857] >>>> >>>> subtract the first equation from the second: >>>> >>>> 999,999*x=142857 => x=142857/999,999=1/7 >>>> >>> >>> To determine whether a number x is rational or not, we can repeatedly subtract >>> rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite >>> steps, then x is rational. Otherwise, x is irrational. >>> If x is a repeating decimal, proposition "repeating decimal is rational" is >>> simply false by sematics. >>> >> >> Let me just ask you two simple questions: >> >> Do you think 1/7 is a rational number or an irrational number? >> > rational > >> What do you think the decimal expansion of 1/7 is? >> > > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure > never terminates which means the conversion is never complete. > It is a repeating decimal. If you try to write it all out, then I agree you will not finish. That does not mean it is not the decimal expansion of 1/7 - the list of multiples of (negative) powers of 10 which sum up to 1/7. You just need a better notation so that you can finish the task - and 0.(142857), as you wrote, is one such notation. (I have no idea what you think the symbol "≒" might mean.) But you agree that 0.(142857) is the decimal expansion of 1/7, even though you could not write it out long-hand, and you agree that 1/7 i rational. And clearly 0.(142857) is a repeating decimal, since that's what the notation means. I can't see how you can still misunderstand this.
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-29 02:23 +0800 |
| Message-ID | <c05df08e5d04c3b3baa1dfd36c2ed23b0c2ca535.camel@gmail.com> |
| In reply to | #118607 |
On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: > On 27/03/2024 17:05, wij wrote: > > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: > > > On 27/03/2024 14:32, wij wrote: > > > > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: > > > > > Am Wed, 27 Mar 2024 20:12:38 +0800 > > > > > schrieb wij <wyniijj5@gmail.com>: > > > > > > > > > > > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: > > > > > > > On 26/03/2024 22:43, wij wrote: > > > > > > > > > > > > > > > > Just repeat the pattern infinitely, then it is irrational. > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) > > > > > > > > cannot terminate, 1/7 != 0.(142857) > > > > > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > I am surprise your math. knowledge is so low worse than teenagers. > > > > > > > > > > Use the standard trick: > > > > > > > > > > x=0.[142857] => 1,000,000*x=142857.[142857] > > > > > > > > > > subtract the first equation from the second: > > > > > > > > > > 999,999*x=142857 => x=142857/999,999=1/7 > > > > > > > > > > > > > To determine whether a number x is rational or not, we can repeatedly subtract > > > > rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite > > > > steps, then x is rational. Otherwise, x is irrational. > > > > If x is a repeating decimal, proposition "repeating decimal is rational" is > > > > simply false by sematics. > > > > > > > > > > Let me just ask you two simple questions: > > > > > > Do you think 1/7 is a rational number or an irrational number? > > > > > rational > > > > > What do you think the decimal expansion of 1/7 is? > > > > > > > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure > > never terminates which means the conversion is never complete. > > > > It is a repeating decimal. If you try to write it all out, then I agree > you will not finish. That does not mean it is not the decimal expansion > of 1/7 - the list of multiples of (negative) powers of 10 which sum up > to 1/7. You just need a better notation so that you can finish the task > - and 0.(142857), as you wrote, is one such notation. > > (I have no idea what you think the symbol "≒" might mean.) > > But you agree that 0.(142857) is the decimal expansion of 1/7, even > though you could not write it out long-hand, and you agree that 1/7 i > rational. And clearly 0.(142857) is a repeating decimal, since that's > what the notation means. > > I can't see how you can still misunderstand this. > You are restating your assertion without proof, again. I have provided mine. (If you say that is you proof, I will say it is invalid).
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-29 11:53 +0100 |
| Message-ID | <uu66j4$8ebj$1@dont-email.me> |
| In reply to | #118610 |
On 28/03/2024 19:23, wij wrote: > On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: >> On 27/03/2024 17:05, wij wrote: >>> On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: >>>> On 27/03/2024 14:32, wij wrote: >>>>> On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >>>>>> Am Wed, 27 Mar 2024 20:12:38 +0800 >>>>>> schrieb wij <wyniijj5@gmail.com>: >>>>>> >>>>>>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>>>>>> On 26/03/2024 22:43, wij wrote: >>>>>>>>> >>>>>>>>> Just repeat the pattern infinitely, then it is irrational. >>>>>>>> >>>>>>>> Nonsense. >>>>>>>> >>>>>>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>>>>>> cannot terminate, 1/7 != 0.(142857) >>>>>>>>> >>>>>>>> >>>>>>>> Nonsense. >>>>>>>> >>>>>>> >>>>>>> I am surprise your math. knowledge is so low worse than teenagers. >>>>>> >>>>>> Use the standard trick: >>>>>> >>>>>> x=0.[142857] => 1,000,000*x=142857.[142857] >>>>>> >>>>>> subtract the first equation from the second: >>>>>> >>>>>> 999,999*x=142857 => x=142857/999,999=1/7 >>>>>> >>>>> >>>>> To determine whether a number x is rational or not, we can repeatedly subtract >>>>> rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite >>>>> steps, then x is rational. Otherwise, x is irrational. >>>>> If x is a repeating decimal, proposition "repeating decimal is rational" is >>>>> simply false by sematics. >>>>> >>>> >>>> Let me just ask you two simple questions: >>>> >>>> Do you think 1/7 is a rational number or an irrational number? >>>> >>> rational >>> >>>> What do you think the decimal expansion of 1/7 is? >>>> >>> >>> When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure >>> never terminates which means the conversion is never complete. >>> >> >> It is a repeating decimal. If you try to write it all out, then I agree >> you will not finish. That does not mean it is not the decimal expansion >> of 1/7 - the list of multiples of (negative) powers of 10 which sum up >> to 1/7. You just need a better notation so that you can finish the task >> - and 0.(142857), as you wrote, is one such notation. >> >> (I have no idea what you think the symbol "≒" might mean.) >> >> But you agree that 0.(142857) is the decimal expansion of 1/7, even >> though you could not write it out long-hand, and you agree that 1/7 i >> rational. And clearly 0.(142857) is a repeating decimal, since that's >> what the notation means. >> >> I can't see how you can still misunderstand this. >> > > You are restating your assertion without proof, again. I have provided mine. > (If you say that is you proof, I will say it is invalid). > > There is no point in giving you a rigorous proof that 0.(142857) is the decimal expansion of 1/7, if that is what you are contesting. To be fully rigorous, it requires an understanding of the definition of the real numbers, sequence limits, and the meaning and validity of operations on infinite sequences. You have demonstrated that you don't understand any of that. You have learned a few of the terms, but failed to understand the concepts. Oh, and it also requires understanding what a proof is, which again is clearly outside your expertise. Ralf gave a proof earlier - it is still in the quoted material above. That is as good as we can get at your level of mathematical understanding. To be more rigorous, we would need to demonstrate that the manipulation (multiplication by a finite integer, and subtraction of sequences) of infinite decimal expansions is valid. That is all standard stuff, known to mathematics students the world over, but you are not nearly ready. You are going to have to go back-track a long way in what you think you know about mathematics. Somewhere along the line in your education, you've got things badly wrong. And instead of stopping up and trying to figure out why everyone else is saying something different from you, or asking your teachers for help, you have battered on with your mistakes, leading you to sillier and steadily less logical conclusions. I think mathematics is a great hobby. It's a shame to see someone spend their time and effort on doing it so badly.
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-29 23:14 +0800 |
| Message-ID | <e4986a133c8c5e79734a56229b21d2fd874a3977.camel@gmail.com> |
| In reply to | #118617 |
On Fri, 2024-03-29 at 11:53 +0100, David Brown wrote: > On 28/03/2024 19:23, wij wrote: > > On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: > > > On 27/03/2024 17:05, wij wrote: > > > > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: > > > > > On 27/03/2024 14:32, wij wrote: > > > > > > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: > > > > > > > Am Wed, 27 Mar 2024 20:12:38 +0800 > > > > > > > schrieb wij <wyniijj5@gmail.com>: > > > > > > > > > > > > > > > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: > > > > > > > > > On 26/03/2024 22:43, wij wrote: > > > > > > > > > > > > > > > > > > > > Just repeat the pattern infinitely, then it is irrational. > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) > > > > > > > > > > cannot terminate, 1/7 != 0.(142857) > > > > > > > > > > > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > > > > > > > I am surprise your math. knowledge is so low worse than teenagers. > > > > > > > > > > > > > > Use the standard trick: > > > > > > > > > > > > > > x=0.[142857] => 1,000,000*x=142857.[142857] > > > > > > > > > > > > > > subtract the first equation from the second: > > > > > > > > > > > > > > 999,999*x=142857 => x=142857/999,999=1/7 > > > > > > > > > > > > > > > > > > > To determine whether a number x is rational or not, we can repeatedly subtract > > > > > > rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite > > > > > > steps, then x is rational. Otherwise, x is irrational. > > > > > > If x is a repeating decimal, proposition "repeating decimal is rational" is > > > > > > simply false by sematics. > > > > > > > > > > > > > > > > Let me just ask you two simple questions: > > > > > > > > > > Do you think 1/7 is a rational number or an irrational number? > > > > > > > > > rational > > > > > > > > > What do you think the decimal expansion of 1/7 is? > > > > > > > > > > > > > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure > > > > never terminates which means the conversion is never complete. > > > > > > > > > > It is a repeating decimal. If you try to write it all out, then I agree > > > you will not finish. That does not mean it is not the decimal expansion > > > of 1/7 - the list of multiples of (negative) powers of 10 which sum up > > > to 1/7. You just need a better notation so that you can finish the task > > > - and 0.(142857), as you wrote, is one such notation. > > > > > > (I have no idea what you think the symbol "≒" might mean.) > > > > > > But you agree that 0.(142857) is the decimal expansion of 1/7, even > > > though you could not write it out long-hand, and you agree that 1/7 i > > > rational. And clearly 0.(142857) is a repeating decimal, since that's > > > what the notation means. > > > > > > I can't see how you can still misunderstand this. > > > > > > > You are restating your assertion without proof, again. I have provided mine. > > (If you say that is you proof, I will say it is invalid). > > > > > > There is no point in giving you a rigorous proof that 0.(142857) is the > decimal expansion of 1/7, if that is what you are contesting. To be > fully rigorous, it requires an understanding of the definition of the > real numbers, sequence limits, and the meaning and validity of > operations on infinite sequences. You have demonstrated that you don't > understand any of that. You have learned a few of the terms, but failed > to understand the concepts. Oh, and it also requires understanding what > a proof is, which again is clearly outside your expertise. > > Ralf gave a proof earlier - it is still in the quoted material above. > That is as good as we can get at your level of mathematical > understanding. To be more rigorous, we would need to demonstrate that > the manipulation (multiplication by a finite integer, and subtraction of > sequences) of infinite decimal expansions is valid. That is all > standard stuff, known to mathematics students the world over, but you > are not nearly ready. > > You are going to have to go back-track a long way in what you think you > know about mathematics. Somewhere along the line in your education, > you've got things badly wrong. And instead of stopping up and trying to > figure out why everyone else is saying something different from you, or > asking your teachers for help, you have battered on with your mistakes, > leading you to sillier and steadily less logical conclusions. > > I think mathematics is a great hobby. It's a shame to see someone spend > their time and effort on doing it so badly. > Have you ever wondered why you cannot prove something you hold true for granted for so long? If you cannot provide a proof, what you said above only make you more a sinner.
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-29 16:48 +0100 |
| Message-ID | <uu6nrm$ce2n$1@dont-email.me> |
| In reply to | #118620 |
On 29/03/2024 16:14, wij wrote: > On Fri, 2024-03-29 at 11:53 +0100, David Brown wrote: >> On 28/03/2024 19:23, wij wrote: >>> On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: >>>> On 27/03/2024 17:05, wij wrote: >>>>> On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: >>>>>> On 27/03/2024 14:32, wij wrote: >>>>>>> On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >>>>>>>> Am Wed, 27 Mar 2024 20:12:38 +0800 >>>>>>>> schrieb wij <wyniijj5@gmail.com>: >>>>>>>> >>>>>>>>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>>>>>>>> On 26/03/2024 22:43, wij wrote: >>>>>>>>>>> >>>>>>>>>>> Just repeat the pattern infinitely, then it is irrational. >>>>>>>>>> >>>>>>>>>> Nonsense. >>>>>>>>>> >>>>>>>>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>>>>>>>> cannot terminate, 1/7 != 0.(142857) >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Nonsense. >>>>>>>>>> >>>>>>>>> >>>>>>>>> I am surprise your math. knowledge is so low worse than teenagers. >>>>>>>> >>>>>>>> Use the standard trick: >>>>>>>> >>>>>>>> x=0.[142857] => 1,000,000*x=142857.[142857] >>>>>>>> >>>>>>>> subtract the first equation from the second: >>>>>>>> >>>>>>>> 999,999*x=142857 => x=142857/999,999=1/7 >>>>>>>> >>>>>>> >>>>>>> To determine whether a number x is rational or not, we can repeatedly subtract >>>>>>> rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite >>>>>>> steps, then x is rational. Otherwise, x is irrational. >>>>>>> If x is a repeating decimal, proposition "repeating decimal is rational" is >>>>>>> simply false by sematics. >>>>>>> >>>>>> >>>>>> Let me just ask you two simple questions: >>>>>> >>>>>> Do you think 1/7 is a rational number or an irrational number? >>>>>> >>>>> rational >>>>> >>>>>> What do you think the decimal expansion of 1/7 is? >>>>>> >>>>> >>>>> When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure >>>>> never terminates which means the conversion is never complete. >>>>> >>>> >>>> It is a repeating decimal. If you try to write it all out, then I agree >>>> you will not finish. That does not mean it is not the decimal expansion >>>> of 1/7 - the list of multiples of (negative) powers of 10 which sum up >>>> to 1/7. You just need a better notation so that you can finish the task >>>> - and 0.(142857), as you wrote, is one such notation. >>>> >>>> (I have no idea what you think the symbol "≒" might mean.) >>>> >>>> But you agree that 0.(142857) is the decimal expansion of 1/7, even >>>> though you could not write it out long-hand, and you agree that 1/7 i >>>> rational. And clearly 0.(142857) is a repeating decimal, since that's >>>> what the notation means. >>>> >>>> I can't see how you can still misunderstand this. >>>> >>> >>> You are restating your assertion without proof, again. I have provided mine. >>> (If you say that is you proof, I will say it is invalid). >>> >>> >> >> There is no point in giving you a rigorous proof that 0.(142857) is the >> decimal expansion of 1/7, if that is what you are contesting. To be >> fully rigorous, it requires an understanding of the definition of the >> real numbers, sequence limits, and the meaning and validity of >> operations on infinite sequences. You have demonstrated that you don't >> understand any of that. You have learned a few of the terms, but failed >> to understand the concepts. Oh, and it also requires understanding what >> a proof is, which again is clearly outside your expertise. >> >> Ralf gave a proof earlier - it is still in the quoted material above. >> That is as good as we can get at your level of mathematical >> understanding. To be more rigorous, we would need to demonstrate that >> the manipulation (multiplication by a finite integer, and subtraction of >> sequences) of infinite decimal expansions is valid. That is all >> standard stuff, known to mathematics students the world over, but you >> are not nearly ready. >> >> You are going to have to go back-track a long way in what you think you >> know about mathematics. Somewhere along the line in your education, >> you've got things badly wrong. And instead of stopping up and trying to >> figure out why everyone else is saying something different from you, or >> asking your teachers for help, you have battered on with your mistakes, >> leading you to sillier and steadily less logical conclusions. >> >> I think mathematics is a great hobby. It's a shame to see someone spend >> their time and effort on doing it so badly. >> > > Have you ever wondered why you cannot prove something you hold true for granted > for so long? Yes, regularly. Sometimes I will then try to find a proof, or look up and learn about the proofs. Sometimes I will have to accept that proving the particular thing is beyond my mathematical skills, or my time and energy, or my interest, and I will defer to accepting that others have proven it. > > If you cannot provide a proof, what you said above only make you more a sinner. > In this particular case, I most certainly /can/ provide a proof. But I can't provide a proof that /you/ would understand. And since writing a proof would be a fair effort, off-topic, and clearly a waste of time since you are impervious to mathematical reasoning, I will not bother. You can look up such proofs online - I'm sure there are countless Youtube videos that will explain it to anyone who is actually interested in learning and not merely trying to claim the whole world is wrong except them.
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-30 00:16 +0800 |
| Message-ID | <b1246e6005f248c318d5f5dc590cafb7a51e9c83.camel@gmail.com> |
| In reply to | #118621 |
On Fri, 2024-03-29 at 16:48 +0100, David Brown wrote: > On 29/03/2024 16:14, wij wrote: > > On Fri, 2024-03-29 at 11:53 +0100, David Brown wrote: > > > On 28/03/2024 19:23, wij wrote: > > > > On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: > > > > > On 27/03/2024 17:05, wij wrote: > > > > > > On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: > > > > > > > On 27/03/2024 14:32, wij wrote: > > > > > > > > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: > > > > > > > > > Am Wed, 27 Mar 2024 20:12:38 +0800 > > > > > > > > > schrieb wij <wyniijj5@gmail.com>: > > > > > > > > > > > > > > > > > > > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: > > > > > > > > > > > On 26/03/2024 22:43, wij wrote: > > > > > > > > > > > > > > > > > > > > > > > > Just repeat the pattern infinitely, then it is irrational. > > > > > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > > > > > As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) > > > > > > > > > > > > cannot terminate, 1/7 != 0.(142857) > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > Nonsense. > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > I am surprise your math. knowledge is so low worse than teenagers. > > > > > > > > > > > > > > > > > > Use the standard trick: > > > > > > > > > > > > > > > > > > x=0.[142857] => 1,000,000*x=142857.[142857] > > > > > > > > > > > > > > > > > > subtract the first equation from the second: > > > > > > > > > > > > > > > > > > 999,999*x=142857 => x=142857/999,999=1/7 > > > > > > > > > > > > > > > > > > > > > > > > > To determine whether a number x is rational or not, we can repeatedly subtract > > > > > > > > rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite > > > > > > > > steps, then x is rational. Otherwise, x is irrational. > > > > > > > > If x is a repeating decimal, proposition "repeating decimal is rational" is > > > > > > > > simply false by sematics. > > > > > > > > > > > > > > > > > > > > > > Let me just ask you two simple questions: > > > > > > > > > > > > > > Do you think 1/7 is a rational number or an irrational number? > > > > > > > > > > > > > rational > > > > > > > > > > > > > What do you think the decimal expansion of 1/7 is? > > > > > > > > > > > > > > > > > > > When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure > > > > > > never terminates which means the conversion is never complete. > > > > > > > > > > > > > > > > It is a repeating decimal. If you try to write it all out, then I agree > > > > > you will not finish. That does not mean it is not the decimal expansion > > > > > of 1/7 - the list of multiples of (negative) powers of 10 which sum up > > > > > to 1/7. You just need a better notation so that you can finish the task > > > > > - and 0.(142857), as you wrote, is one such notation. > > > > > > > > > > (I have no idea what you think the symbol "≒" might mean.) > > > > > > > > > > But you agree that 0.(142857) is the decimal expansion of 1/7, even > > > > > though you could not write it out long-hand, and you agree that 1/7 i > > > > > rational. And clearly 0.(142857) is a repeating decimal, since that's > > > > > what the notation means. > > > > > > > > > > I can't see how you can still misunderstand this. > > > > > > > > > > > > > You are restating your assertion without proof, again. I have provided mine. > > > > (If you say that is you proof, I will say it is invalid). > > > > > > > > > > > > > > There is no point in giving you a rigorous proof that 0.(142857) is the > > > decimal expansion of 1/7, if that is what you are contesting. To be > > > fully rigorous, it requires an understanding of the definition of the > > > real numbers, sequence limits, and the meaning and validity of > > > operations on infinite sequences. You have demonstrated that you don't > > > understand any of that. You have learned a few of the terms, but failed > > > to understand the concepts. Oh, and it also requires understanding what > > > a proof is, which again is clearly outside your expertise. > > > > > > Ralf gave a proof earlier - it is still in the quoted material above. > > > That is as good as we can get at your level of mathematical > > > understanding. To be more rigorous, we would need to demonstrate that > > > the manipulation (multiplication by a finite integer, and subtraction of > > > sequences) of infinite decimal expansions is valid. That is all > > > standard stuff, known to mathematics students the world over, but you > > > are not nearly ready. > > > > > > You are going to have to go back-track a long way in what you think you > > > know about mathematics. Somewhere along the line in your education, > > > you've got things badly wrong. And instead of stopping up and trying to > > > figure out why everyone else is saying something different from you, or > > > asking your teachers for help, you have battered on with your mistakes, > > > leading you to sillier and steadily less logical conclusions. > > > > > > I think mathematics is a great hobby. It's a shame to see someone spend > > > their time and effort on doing it so badly. > > > > > > > Have you ever wondered why you cannot prove something you hold true for granted > > for so long? > > Yes, regularly. Sometimes I will then try to find a proof, or look up > and learn about the proofs. Sometimes I will have to accept that > proving the particular thing is beyond my mathematical skills, or my > time and energy, or my interest, and I will defer to accepting that > others have proven it. > > > > > If you cannot provide a proof, what you said above only make you more a sinner. > > > > In this particular case, I most certainly /can/ provide a proof. But I > can't provide a proof that /you/ would understand. And since writing a > proof would be a fair effort, off-topic, and clearly a waste of time > since you are impervious to mathematical reasoning, I will not bother. > You can look up such proofs online - I'm sure there are countless > Youtube videos that will explain it to anyone who is actually interested > in learning and not merely trying to claim the whole world is wrong > except them. > Not the whole world, you can see some on the internet claiming "0.999...!=1", although the proof is also invalid. And, in every generation, every kid (developed IQ) in school will keep wondering why 1/3=0.333... 'will stop' and why the the number very close to the left of 1 is not 0.999.... ! Have you wondered if 1/3=0.333..., the conversion algorithm is theoretically flawed?
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-03-29 15:43 -0700 |
| Message-ID | <uu7g6a$i04u$6@dont-email.me> |
| In reply to | #118622 |
On 3/29/2024 9:16 AM, wij wrote: [...] > Have you wondered if 1/3=0.333..., the conversion algorithm is theoretically flawed? Yawn.
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-30 15:44 +0100 |
| Message-ID | <uu98gj$123h1$1@dont-email.me> |
| In reply to | #118622 |
On 29/03/2024 17:16, wij wrote: > On Fri, 2024-03-29 at 16:48 +0100, David Brown wrote: >> On 29/03/2024 16:14, wij wrote: >>> On Fri, 2024-03-29 at 11:53 +0100, David Brown wrote: >>>> On 28/03/2024 19:23, wij wrote: >>>>> On Thu, 2024-03-28 at 18:16 +0100, David Brown wrote: >>>>>> On 27/03/2024 17:05, wij wrote: >>>>>>> On Wed, 2024-03-27 at 16:02 +0100, David Brown wrote: >>>>>>>> On 27/03/2024 14:32, wij wrote: >>>>>>>>> On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >>>>>>>>>> Am Wed, 27 Mar 2024 20:12:38 +0800 >>>>>>>>>> schrieb wij <wyniijj5@gmail.com>: >>>>>>>>>> >>>>>>>>>>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>>>>>>>>>> On 26/03/2024 22:43, wij wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> Just repeat the pattern infinitely, then it is irrational. >>>>>>>>>>>> >>>>>>>>>>>> Nonsense. >>>>>>>>>>>> >>>>>>>>>>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>>>>>>>>>> cannot terminate, 1/7 != 0.(142857) >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Nonsense. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> I am surprise your math. knowledge is so low worse than teenagers. >>>>>>>>>> >>>>>>>>>> Use the standard trick: >>>>>>>>>> >>>>>>>>>> x=0.[142857] => 1,000,000*x=142857.[142857] >>>>>>>>>> >>>>>>>>>> subtract the first equation from the second: >>>>>>>>>> >>>>>>>>>> 999,999*x=142857 => x=142857/999,999=1/7 >>>>>>>>>> >>>>>>>>> >>>>>>>>> To determine whether a number x is rational or not, we can repeatedly subtract >>>>>>>>> rational numbers a? from x. If x-a1-a2-a3-...=0 can be verified in finite >>>>>>>>> steps, then x is rational. Otherwise, x is irrational. >>>>>>>>> If x is a repeating decimal, proposition "repeating decimal is rational" is >>>>>>>>> simply false by sematics. >>>>>>>>> >>>>>>>> >>>>>>>> Let me just ask you two simple questions: >>>>>>>> >>>>>>>> Do you think 1/7 is a rational number or an irrational number? >>>>>>>> >>>>>>> rational >>>>>>> >>>>>>>> What do you think the decimal expansion of 1/7 is? >>>>>>>> >>>>>>> >>>>>>> When converting 1/7 to decimal, the result ≒ 0.(142857), the procedure >>>>>>> never terminates which means the conversion is never complete. >>>>>>> >>>>>> >>>>>> It is a repeating decimal. If you try to write it all out, then I agree >>>>>> you will not finish. That does not mean it is not the decimal expansion >>>>>> of 1/7 - the list of multiples of (negative) powers of 10 which sum up >>>>>> to 1/7. You just need a better notation so that you can finish the task >>>>>> - and 0.(142857), as you wrote, is one such notation. >>>>>> >>>>>> (I have no idea what you think the symbol "≒" might mean.) >>>>>> >>>>>> But you agree that 0.(142857) is the decimal expansion of 1/7, even >>>>>> though you could not write it out long-hand, and you agree that 1/7 i >>>>>> rational. And clearly 0.(142857) is a repeating decimal, since that's >>>>>> what the notation means. >>>>>> >>>>>> I can't see how you can still misunderstand this. >>>>>> >>>>> >>>>> You are restating your assertion without proof, again. I have provided mine. >>>>> (If you say that is you proof, I will say it is invalid). >>>>> >>>>> >>>> >>>> There is no point in giving you a rigorous proof that 0.(142857) is the >>>> decimal expansion of 1/7, if that is what you are contesting. To be >>>> fully rigorous, it requires an understanding of the definition of the >>>> real numbers, sequence limits, and the meaning and validity of >>>> operations on infinite sequences. You have demonstrated that you don't >>>> understand any of that. You have learned a few of the terms, but failed >>>> to understand the concepts. Oh, and it also requires understanding what >>>> a proof is, which again is clearly outside your expertise. >>>> >>>> Ralf gave a proof earlier - it is still in the quoted material above. >>>> That is as good as we can get at your level of mathematical >>>> understanding. To be more rigorous, we would need to demonstrate that >>>> the manipulation (multiplication by a finite integer, and subtraction of >>>> sequences) of infinite decimal expansions is valid. That is all >>>> standard stuff, known to mathematics students the world over, but you >>>> are not nearly ready. >>>> >>>> You are going to have to go back-track a long way in what you think you >>>> know about mathematics. Somewhere along the line in your education, >>>> you've got things badly wrong. And instead of stopping up and trying to >>>> figure out why everyone else is saying something different from you, or >>>> asking your teachers for help, you have battered on with your mistakes, >>>> leading you to sillier and steadily less logical conclusions. >>>> >>>> I think mathematics is a great hobby. It's a shame to see someone spend >>>> their time and effort on doing it so badly. >>>> >>> >>> Have you ever wondered why you cannot prove something you hold true for granted >>> for so long? >> >> Yes, regularly. Sometimes I will then try to find a proof, or look up >> and learn about the proofs. Sometimes I will have to accept that >> proving the particular thing is beyond my mathematical skills, or my >> time and energy, or my interest, and I will defer to accepting that >> others have proven it. >> >>> >>> If you cannot provide a proof, what you said above only make you more a sinner. >>> >> >> In this particular case, I most certainly /can/ provide a proof. But I >> can't provide a proof that /you/ would understand. And since writing a >> proof would be a fair effort, off-topic, and clearly a waste of time >> since you are impervious to mathematical reasoning, I will not bother. >> You can look up such proofs online - I'm sure there are countless >> Youtube videos that will explain it to anyone who is actually interested >> in learning and not merely trying to claim the whole world is wrong >> except them. >> > > Not the whole world, you can see some on the internet claiming "0.999...!=1", > although the proof is also invalid. Of course there are no valid proofs that 0.999... != 1, since it 0.999... is equal to 1. But there are folks on the internet claiming the earth is flat, birds are not real, and every other bit of nonsense you could imagine. > And, in every generation, every kid > (developed IQ) in school will keep wondering why 1/3=0.333... 'will stop' I've never known anyone to wonder that - any kid who learns about this learns that it does /not/ stop. That's what the three dots mean. But maybe you didn't write quite what you meant to write here. > and > why the the number very close to the left of 1 is not 0.999.... ! Certainly people wonder about things like this. They wonder if 0.999... really is the same as 1, and how could they prove it. (It /is/ the same, and the proof is easy.) They wonder if there is a number "just to the left of 1", and what it might be. (There is no such number.) /Wondering/ about these things, and being curious about them, is great. Claiming falsehoods about them, writing nonsense and calling it a "proof", is /not/ great. > > Have you wondered if 1/3=0.333..., the conversion algorithm is theoretically flawed? > I have wondered about a lot of things, including things I know to be easily proven true - such as that 1/3 = 0.333... And I have challenged things like this, checked that /I/ can prove them true, or wondered if there were alternative definitions of real numbers, decimal representations, basic arithmetic, etc., in which the results are different. It turns out that if you want some useful fundamental properties to be true (such as reals being a complete ordered field), some results are inevitable. That is how you do mathematics.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-03-29 15:40 -0700 |
| Message-ID | <uu7g1c$i04u$5@dont-email.me> |
| In reply to | #118620 |
On 3/29/2024 8:14 AM, wij wrote: [...] > Have you ever wondered why you cannot prove something you hold true for granted > for so long? > > If you cannot provide a proof, what you said above only make you more a sinner. Oh common. You know better. Well, at least I think you do.
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2024-03-29 11:35 -0700 |
| Message-ID | <87msqgsx73.fsf@nosuchdomain.example.com> |
| In reply to | #118617 |
David Brown <david.brown@hesbynett.no> writes:
[...]
> I think mathematics is a great hobby. It's a shame to see someone
> spend their time and effort on doing it so badly.
It's also a shame to see someone engaging here in a discussion that has
nothing to do with C++. David, if you must feed this particular troll,
I suggest doing so in comp.theory.
*You don't have to reply to everything.*
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-30 15:49 +0100 |
| Message-ID | <uu98pc$123h1$2@dont-email.me> |
| In reply to | #118623 |
On 29/03/2024 19:35, Keith Thompson wrote: > David Brown <david.brown@hesbynett.no> writes: > [...] >> I think mathematics is a great hobby. It's a shame to see someone >> spend their time and effort on doing it so badly. > > It's also a shame to see someone engaging here in a discussion that has > nothing to do with C++. David, if you must feed this particular troll, > I suggest doing so in comp.theory. > > *You don't have to reply to everything.* > It is Easter, and Usenet traffic is low. No, I don't have to reply to everything (and I don't - I have replied to very few of wij's broken maths threads), and this thread will soon die away. I am trying to get some idea of why wij thinks the way he does, and perhaps even help him think differently (though that's quite optimistic).
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-30 23:14 +0800 |
| Message-ID | <0c99f8d4f3bfc9d800e7f6db0a69b8dbd99b44e1.camel@gmail.com> |
| In reply to | #118635 |
On Sat, 2024-03-30 at 15:49 +0100, David Brown wrote: > On 29/03/2024 19:35, Keith Thompson wrote: > > David Brown <david.brown@hesbynett.no> writes: > > [...] > > > I think mathematics is a great hobby. It's a shame to see someone > > > spend their time and effort on doing it so badly. > > > > It's also a shame to see someone engaging here in a discussion that has > > nothing to do with C++. David, if you must feed this particular troll, > > I suggest doing so in comp.theory. > > > > *You don't have to reply to everything.* > > > > It is Easter, and Usenet traffic is low. No, I don't have to reply to > everything (and I don't - I have replied to very few of wij's broken > maths threads), and this thread will soon die away. I am trying to get > some idea of why wij thinks the way he does, and perhaps even help him > think differently (though that's quite optimistic). > Persuade me and readers with proof, otherwise you lie or spread lies (from the moment)
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-30 19:26 +0100 |
| Message-ID | <uu9lgr$15414$1@dont-email.me> |
| In reply to | #118636 |
On 30/03/2024 16:14, wij wrote: > On Sat, 2024-03-30 at 15:49 +0100, David Brown wrote: >> On 29/03/2024 19:35, Keith Thompson wrote: >>> David Brown <david.brown@hesbynett.no> writes: >>> [...] >>>> I think mathematics is a great hobby. It's a shame to see someone >>>> spend their time and effort on doing it so badly. >>> >>> It's also a shame to see someone engaging here in a discussion that has >>> nothing to do with C++. David, if you must feed this particular troll, >>> I suggest doing so in comp.theory. >>> >>> *You don't have to reply to everything.* >>> >> >> It is Easter, and Usenet traffic is low. No, I don't have to reply to >> everything (and I don't - I have replied to very few of wij's broken >> maths threads), and this thread will soon die away. I am trying to get >> some idea of why wij thinks the way he does, and perhaps even help him >> think differently (though that's quite optimistic). >> > > Persuade me and readers with proof, otherwise you lie or spread lies (from the moment) > You were given a proof, but rejected it for no reason other than it showed that your jumble of claims was incorrect. Thus I don't think there is any point in trying to give more detailed proofs. But if you like, I can give some links to other people's proofs - starting with proving that 0.999... equals 1. If you agree with these, maybe we can move on to proving that 1/3 equals 0.33... repeating, and then further onto showing that repeating decimals are rational. So let me know which of these links you agree with, or disagree with (preferably with reasons or justification for disagreeing with them). <https://en.wikipedia.org/wiki/0.999...> <https://www.purplemath.com/modules/howcan1.htm> <https://brilliant.org/wiki/is-0999-equal-1/> (I don't need to persuade any other readers - they already know this stuff.) And if you think I am lying, you can add lying to your list of concepts that you don't understand.
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| From | wij <wyniijj5@gmail.com> |
|---|---|
| Date | 2024-03-31 03:30 +0800 |
| Message-ID | <1925c514508b72d3f0a5727e4793697b3e065ee0.camel@gmail.com> |
| In reply to | #118637 |
On Sat, 2024-03-30 at 19:26 +0100, David Brown wrote: > On 30/03/2024 16:14, wij wrote: > > On Sat, 2024-03-30 at 15:49 +0100, David Brown wrote: > > > On 29/03/2024 19:35, Keith Thompson wrote: > > > > David Brown <david.brown@hesbynett.no> writes: > > > > [...] > > > > > I think mathematics is a great hobby. It's a shame to see someone > > > > > spend their time and effort on doing it so badly. > > > > > > > > It's also a shame to see someone engaging here in a discussion that has > > > > nothing to do with C++. David, if you must feed this particular troll, > > > > I suggest doing so in comp.theory. > > > > > > > > *You don't have to reply to everything.* > > > > > > > > > > It is Easter, and Usenet traffic is low. No, I don't have to reply to > > > everything (and I don't - I have replied to very few of wij's broken > > > maths threads), and this thread will soon die away. I am trying to get > > > some idea of why wij thinks the way he does, and perhaps even help him > > > think differently (though that's quite optimistic). > > > > > > > Persuade me and readers with proof, otherwise you lie or spread lies (from the moment) > > > > You were given a proof, but rejected it for no reason other than it > showed that your jumble of claims was incorrect. Thus I don't think > there is any point in trying to give more detailed proofs. But if you > like, I can give some links to other people's proofs - starting with > proving that 0.999... equals 1. If you agree with these, maybe we can > move on to proving that 1/3 equals 0.33... repeating, and then further > onto showing that repeating decimals are rational. So let me know which > of these links you agree with, or disagree with (preferably with reasons > or justification for disagreeing with them). > > <https://en.wikipedia.org/wiki/0.999...> > <https://www.purplemath.com/modules/howcan1.htm> > <https://brilliant.org/wiki/is-0999-equal-1/> > > > (I don't need to persuade any other readers - they already know this stuff.) > > > And if you think I am lying, you can add lying to your list of concepts > that you don't understand. > > I cannot read English fast. I will pick the one proof not in my proof. Archimedean property just states that infinitesmal does not exit, IIUC. It is an assertion, not a proof. But I think, if infinitesimal does not exit, what did those calculus pioneers baffled at? (I just have a thought, with Archimedean property, you cannot say "infinite repeating" because there is no 1/∞, this applies to the decimal representation of √2) The second one's proof depends on magic trick to make people believe, but neither a valid proof. I have shown how the magic works in my post. The third one's link, ... the same. You saw my Simple Enough Proof For Kids (kids know what the Emperor's Cloth is) and can't disprove it or prove your belief. What should I interpret if you attack too hard?
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-03-27 13:29 -0700 |
| Message-ID | <uu1vii$31us4$2@dont-email.me> |
| In reply to | #118573 |
On 3/27/2024 6:32 AM, wij wrote: > On Wed, 2024-03-27 at 13:57 +0100, Ralf Goertz wrote: >> Am Wed, 27 Mar 2024 20:12:38 +0800 >> schrieb wij <wyniijj5@gmail.com>: >> >>> On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >>>> On 26/03/2024 22:43, wij wrote: >>>>> >>>>> Just repeat the pattern infinitely, then it is irrational. >>>> >>>> Nonsense. >>>> >>>>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>>>> cannot terminate, 1/7 != 0.(142857) >>>>> >>>> >>>> Nonsense. >>>> >>> >>> I am surprise your math. knowledge is so low worse than teenagers. >> >> Use the standard trick: >> >> x=0.[142857] => 1,000,000*x=142857.[142857] >> >> subtract the first equation from the second: >> >> 999,999*x=142857 => x=142857/999,999=1/7 >> > > To determine whether a number x is rational or not,[...] Check for a period...
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2024-03-27 15:51 +0100 |
| Message-ID | <uu1bp6$2tbcd$1@dont-email.me> |
| In reply to | #118571 |
On 27/03/2024 13:12, wij wrote: > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >> On 26/03/2024 22:43, wij wrote: >>> On Tue, 2024-03-26 at 13:13 -0700, Chris M. Thomasson wrote: >>>> On 3/26/2024 7:51 AM, wij wrote: >>>> [...] >>>> >>>> Repeating decimals are rational, say >>>> >>>> 0.142857 142857 142857 >>>> >>>> That is just 1 / 7 represented in base 10. >>>> >>>> Now, think of using a TRNG to create each digit... >>>> >>>> That would be, irrational... ;^) >>> >>> Just repeat the pattern infinitely, then it is irrational. >> >> Nonsense. >> >>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>> cannot terminate, 1/7 != 0.(142857) >>> >> >> Nonsense. >> > > I am surprise your math. knowledge is so low worse than teenagers. > It's a long time ago and hard to be sure, but I believe I knew that real numbers were rational if and only if their decimal expansion was repeating before I was a teenager. And I don't believe that rational numbers or decimal expansions have changed their nature since then. (And as a maths student I wrote an essay on a derivation of the real numbers from the axioms of Zermelo-Fraenkel set theory, proving each step along the way, proving the equivalence between constructions from decimal - or n-ary - representations to constructions based on completing the rationals, proving the existence of irrational numbers, and establishing the cardinality of the real numbers. I might be a bit out of practice, but I know what I am talking about.) If you hold strange views on a mathematical topic that runs contrary to the established mainstream, especially something so simple and non-contentious, you have to be prepared to be treated as a fool and ridiculed as a flat-earther or a trisector. But just for your benefit, I had a quick look at the start of your "RealNumber-en.txt" file - the section on Real Numbers. 1. /You/ don't get to define real numbers. That is a well-established term in mathematics, and you don't get to replace it with waffle-worded text. 2. In mathematics, you don't get to say "a definition is not provided" and then "this definition implies ...". Make /rigorous/ definitions, and /prove/ their definitions. What you are writing here is not mathematics - it's a C-grade response to a high-school test question "What is a real number?". 3. You cannot claim what this definition (such as it is) says about irrational numbers, when you have not said what rational or irrational numbers are. Since you are using your own broken definition for reals, who knows what mistaken ideas you might have about rationals and irrationals. 4. Arithmetic on repeating decimals is well defined, and if x = 0.999... then 10.x is 9 + x. This /is/ provable. 5. Please don't try and talk about axioms. You are /very/ far from that level of rigour. 6. Even if your claim that 0.999... != 1 were true, and even if you had proven it, it would not have the implications you are claiming. 7. Noting that the rationals are closed under subtraction has not the slightest bearing on anything that you have been claiming. It's plausible that it might be involved in a step of the proof of your claims - if such a proof were possible. But you haven't even made the vaguest suggestions of a proof - you simply throw out your claims and expect them to be believed. (The rest of the document is too jumbled and unclear to critique. I appreciate that English is not your first language, but you seem to be able to write it well enough when you try, so I blame your mathematics, not your language skills.) I expect you've been told all of this before. >> Simply stating random things does not make them so. >> >> I recommend you stick to C++ in this C++ newsgroup. >> > > I know. You 'occupied' c/c++ forum and think you are speech police. I have not "occupied" anything. This is a newsgroup primarily concerned with discussions of C++ - that's in the name of the group. I also recommend you stick to C++ because you apparently have an interest in and knowledge of C++, and as far as I have noticed, you talk sensibly about the language. > For now, this discussion is mainly in comp.theory You started a new thread in comp.lang.c++. I don't know what there might or might not be in comp.theory - anything there is irrelevant to this discussion. (I can't see how your post is remotely on-topic for computational theory either.) > But you have shown your knowledge is so so low, don't go there waste our time. I don't follow comp.theory. But I have seen a few threads over the years which have "leaked" from there to groups that I do follow, and I feel confident in guessing that few people there share your ideas about real numbers. > >> As for your maths, you'd do better learning some basics of the >> mathematics of real numbers and rational numbers, and that being able to >> find the Unicode characters for some logic symbols does not mean you >> understand how to write a proof. >> >> > >
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-03-27 21:52 -0700 |
| Message-ID | <uu2t1j$3c8ci$8@dont-email.me> |
| In reply to | #118571 |
On 3/27/2024 5:12 AM, wij wrote: > On Wed, 2024-03-27 at 12:50 +0100, David Brown wrote: >> On 26/03/2024 22:43, wij wrote: >>> On Tue, 2024-03-26 at 13:13 -0700, Chris M. Thomasson wrote: >>>> On 3/26/2024 7:51 AM, wij wrote: >>>> [...] >>>> >>>> Repeating decimals are rational, say >>>> >>>> 0.142857 142857 142857 >>>> >>>> That is just 1 / 7 represented in base 10. >>>> >>>> Now, think of using a TRNG to create each digit... >>>> >>>> That would be, irrational... ;^) >>> >>> Just repeat the pattern infinitely, then it is irrational. >> >> Nonsense. >> >>> As said "∀x,a∈ℚ, x-a∈ℚ", if the subtraction a= 142857/10^(6*i) >>> cannot terminate, 1/7 != 0.(142857) >>> >> >> Nonsense. >> > > I am surprise your math. knowledge is so low worse than teenagers. Oh wow. What made you say that? Just a bit interested? Humm... > >> Simply stating random things does not make them so. >> >> I recommend you stick to C++ in this C++ newsgroup. >> > > I know. You 'occupied' c/c++ forum and think you are speech police. > For now, this discussion is mainly in comp.theory > But you have shown your knowledge is so so low, don't go there waste our time. > >> As for your maths, you'd do better learning some basics of the >> mathematics of real numbers and rational numbers, and that being able to >> find the Unicode characters for some logic symbols does not mean you >> understand how to write a proof. >> >> > >
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| From | Paavo Helde <eesnimi@osa.pri.ee> |
|---|---|
| Date | 2024-03-26 23:51 +0200 |
| Message-ID | <utvg0s$2ce32$1@dont-email.me> |
| In reply to | #118558 |
26.03.2024 22:13 Chris M. Thomasson kirjutas: > On 3/26/2024 7:51 AM, wij wrote: > [...] > > Repeating decimals are rational, say > > 0.142857 142857 142857 > > That is just 1 / 7 represented in base 10. > > Now, think of using a TRNG to create each digit... > > That would be, irrational... ;^) Any number represented by stored digits on Earth has finite number of digits (because Earth is finite) and therefore is rational, regardless of how the digits are generated. If you want to represent irrational numbers you need to use some other encoding schema, e.g. "sqrt(2)" (8 bytes, voila!).
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