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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Newsgroups | sci.logic, comp.ai.philosophy, comp.theory, sci.math |
| Subject | Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] |
| Date | 2019-09-16 09:15 -0600 |
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <qlo8uj$db7$2@dont-email.me> (permalink) |
| References | (7 earlier) <oNudndY5IKcOR-fAnZ2dnUU7-T_NnZ2d@giganews.com> <qlfj5b$pbl$1@adenine.netfront.net> <zf2dnakes7ajNObAnZ2dnUU7-W_NnZ2d@giganews.com> <qlkrir$1iva$1@adenine.netfront.net> <n9-dnX44ueOHP-LAnZ2dnUU7-fvNnZ2d@giganews.com> |
Cross-posted to 4 groups.
On 2019-09-16 8:54 a.m., peteolcott wrote:
> On 9/15/2019 3:09 AM, Juha Nieminen wrote:
>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>> On 9/13/2019 3:14 AM, Juha Nieminen wrote:
>>>> In comp.lang.c++ peteolcott <Here@home> wrote:
>>>>> There is a contiguous set of points between (3.0, 4.0].
>>>>> There is a first point in that interval, let's call it X.
>>>>
>>>> No, there isn't. Such a point doesn't exist.
>>>>
>>>> Learn some number theory, will you?
>>>>
>>>
>>> APPARENTLY I AM RIGHT AND YOU ARE WRONG!!!
>>>
>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment
>>
>> You are right and I'm wrong, even though that website does not
>> say what you are saying?
>>
>> It doesn't matter how many arguments you present or how much you
>> shout, it will not make "the smallest real number larger than 3"
>> to start to exist.
>>
>
> The length of this interval is exactly 3.0
> (0.0, 3.0]
> The smallest real number larger than 0.0 is its first point.
>
> The length of this interval is exactly one geometric point longer than 3.0
> [0.0, 3.0]
And points are zero-dimensional. They have no length.
> If we limit the specified points in the intervals to integers then:
> (0.0, 3.0] specifies: {1,2,3}
> [0.0, 3.0] specifies: {0,1,2,3}
> Proving that the above intervals are not the same length.
Claims about the integers don't carry over to the reals. As a trivial
example, the integer 1 is not divisible by 2. The real number 1.0 is.
André
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Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:54 -0500 Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:15 -0600 Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Fred <Fred@nowhere.invalid> - 2019-09-16 16:24 +0100 Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] George Greene <greeneg@email.unc.edu> - 2019-09-16 14:24 -0700
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