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Re: Theorem: There are at least ∞^4 integers in 2 dimensions.

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On 18/11/2020 13:41, Richard Heathfield wrote:
> On 17/11/2020 17:25, Ben Bacarisse wrote:
>> Richard Heathfield <rjh@cpax.org.uk> writes:
>>
>>> On 17/11/2020 06:09, K R wrote:
>>>> Lets look shapes with 3,4,5,6,... angles.
>>>> They have inside ∞ crosses. Because by dividing areas with 2, we get
>>>> ∞ points.
>>>> Lets begin with 2 line connected shapes with 3 and 4 angles.
>>>> We can continue to N shapes.
>>>> Now lets start to go around these shapes with connecting shapes.
>>>> Process can continue forever.
>>>> So we get number N*∞*∞*∞ points.
>>>> The biggest integer is ∞, so there are ∞^4 integers.
>>>
>>> No, ∞ is not an integer. There are infinitely many integers, and
>>> therefore there can be no biggest integer.
>>
>> That makes it sound like it is the infinitude itself that leads to the
>> conclusion, but there are lots of infinite sets with a largest element.
> 
> Yes. The set of negative integers, for example; or the set of reals
> between 0 and 1.
> 

In fact, there are 2 ^ 2 ^ ∞ infinite sets of real numbers with a
largest element.  That's ℶ₂, which is quite big.

>>> This is easily proved by reductio. If we assume there is a biggest
>>> integer I, we can immediately disprove the assumption by adding 1 to I
>>> to form a new integer J that is 1 larger than I.
>>
>> This is what leads to the conclusion: the axioms for the > relation.
>>
>>> Therefore I is not
>>> the biggest integer, even if we (quite improperly) assign ∞ to I.
>>
>> (Oh, and hi.  Haven't seen you around for ages.)
> 
> (Yeah, hi. I'm around, but mostly here, on sci.crypt, and on
> rec.puzzles, all three of which are low-traffic - or low-signal, anyway.
> I stopped bothering with clc when it started morphing into a religious
> debating forum. I haven't been back to check whether that trend continued.)
> 

There's not been much religion on c.l.c. in a while (unless you count
the schism between C and C++ as a religious battle).  But it turns up
occasionally, and there are always some trolls and other less helpful
posters.  (Mind you, last time I told you there had been few religious
posts in c.l.c., and you subscribed again, Rick followed you - by
coincidence, I assume.)

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Theorem: There are at least ∞^4 integers in 2 dimensions. K R <ownerofachattingportal@gmail.com> - 2020-11-16 22:09 -0800
  Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-17 13:10 +0000
    Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-11-17 17:25 +0000
      Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-18 12:41 +0000
        Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 14:58 +0100
          Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Khritjan Robam <hrrobam@gmail.com> - 2020-11-18 06:01 -0800
          Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-18 14:42 +0000
            Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 16:43 +0100
              Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-18 18:59 +0000
                Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 21:39 +0100
    Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-17 22:36 +0100
      Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-18 12:50 +0000
        Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 15:27 +0100
          Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Richard Heathfield <rjh@cpax.org.uk> - 2020-11-18 14:50 +0000
          Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-11-18 15:44 +0000
            Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 18:09 +0100
              Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Peter <peterxpercival@hotmail.com> - 2020-11-18 18:00 +0000
                Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 21:42 +0100
          Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Peter <peterxpercival@hotmail.com> - 2020-11-18 17:58 +0000
            Re: Theorem: There are at least ∞^4 integers in 2 dimensions. David Brown <david.brown@hesbynett.no> - 2020-11-18 21:46 +0100
    Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Melzzzzz <Melzzzzz@zzzzz.com> - 2020-11-19 03:49 +0000
      Re: Theorem: There are at least ∞^4 integers in 2 dimensions. Khrictian Robam <hrrobam@gmail.com> - 2020-11-19 01:12 -0800

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