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

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On 17/11/2020 21:36, David Brown wrote:
> On 17/11/2020 14:10, Richard Heathfield wrote:
>> 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. 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. Therefore I is not the biggest integer, even if we
>> (quite improperly) assign ∞ to I.
>>
> 
> It's nice to see someone trying to post something other than spam in
> this group (and nice to hear you are still around, Richard).
> Unfortunately, you are responding to a spambot, not a person, and the
> original post made no sense.
> 
> If you'd like to talk about infinities, however, I'm game - it's always
> a fun subject (though only vaguely on-topic here).  We could start by
> proving that ∞⁴ is equal to ∞.

I just tried to do that, but what I actually proved (in text that I've 
now deleted) is that there are as many fourth powers of natural numbers 
as there are natural numbers, which is (a) obvious, and (b) not quite 
the same thing as proving that ∞⁴ = ∞ - or at least, if it *is* the same 
thing, I don't quite see why.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

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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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