Re: 2N=E

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

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

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

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?

>
For instance 2 = 2 wrt the vise versa comment.

2 ≠ {2}
I have greatly sinned against Mr Rafters' advice,
but my reason for having done so  is to make
my posts sound as much like WM's posts as I can,
in order to make mine harder to shrug off as
talking about something else.
⎛ One can debate the wisdom of
⎜ trying to actually communicate with WM,
⎝ but, for what it's worth, that's where I am.
Notwithstanding my own behavior,
I agree with Mr Rafters.
2 is an even prime.
One of {2} is an even prime.
Each of {2} is an even prime.
All and only even primes are in non.empty {2}.
Tat seems excessive in the case of {2}
but the same language allows us to finitely.speak of
(each of) uncountably.infinitely.many points in ℝ
Not.doing what I and WM do
is more a matter of clarity than of correctness.
Actual claims are in Math, not English.
But clarity is no small matter.