Re: 2N=E

on 11/4/2024, Chris M. Thomasson supposed :

On 11/4/2024 1:26 AM, Chris M. Thomasson wrote:

On 11/4/2024 12:45 AM, FromTheRafters wrote:

Chris M. Thomasson pretended :

On 11/3/2024 2:40 PM, Chris M. Thomasson wrote:

On 11/3/2024 3:56 AM, WM wrote:

On 03.11.2024 09:50, joes wrote:

pparently you do think that there is a
natural n such that 2^n is infinite.

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If all naturals are there, then no further one is available.

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Sigh. There are infinite natural numbers, there is no last largest one.

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I should say infinitely many natural numbers... Sorry! ;^o
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Damn it. :^)

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Yeah, it is best to use the words 'set of' when 'all' is invoked. The set of all natural numbers is infinite while each and every one of the elements is finite. In that sense (the set of) 'all' is different from 'each' and 'every'.

 Each and every natural number is in all of them and vise versa? Fair enough?

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For instance 2 = 2 wrt the vise versa comment.

All attendees of the dinner went to an after party, each and every one of them got sloshed. This indicates that 'each and every' equals 'all' in normal parlance. Not the same in set theory, 'all' means 'each and every element' taken as a single entity called a set. Such set can have different properties from the elements belonging to it.
So, I'm at odds with the vice versa comment unless it is meant as normal parlance.