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

From	David Brown <david.brown@hesbynett.no>
Newsgroups	comp.programming
Subject	Re: Theorem: There are at least ∞^4 integers in 2 dimensions.
Date	2020-11-18 16:43 +0100
Organization	A noiseless patient Spider
Message-ID	<rp3feb$52g$1@dont-email.me> (permalink)
References	(1 earlier) <rp0i4m$4hq$1@dont-email.me> <87pn4bj3p1.fsf@bsb.me.uk> <rp34ps$jum$1@dont-email.me> <rp39a4$m0i$1@dont-email.me> <rp3bru$a0o$1@dont-email.me>

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On 18/11/2020 15:42, Richard Heathfield wrote:
> On 18/11/2020 13:58, David Brown wrote:
>> 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.
> 
> Did you remember the set of real numbers between 19.00041 and 23.00043?

Yes, it's in there.

> It's easily overlooked. You'd better check your list; if it's not there,
> add it on, and that would make 2 ^ 2 ^ ∞ + 1, which is ever so slightly
> bigger.
> 

The weird thing about infinities is the difference between cardinals
such as ℵ₀ and ordinals such as 𝜔 :  2 ^ 2 ^ ℵ₀ + 1 is the same size as
2 ^ 2 ^ ℵ₀ + 1, while  2 ^ 2 ^ 𝜔 + 1 is different from (and comes just
after) 2 ^ 2 ^ 𝜔.

Thread

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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