Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 11/03/2024 01:21 PM, Richard Damon wrote:

On 11/3/24 7:47 AM, WM wrote:

On 03.11.2024 09:52, joes wrote:

Am Sat, 02 Nov 2024 18:42:15 +0100 schrieb WM:

On 02.11.2024 14:50, Moebius wrote:

Am 02.11.2024 um 14:21 schrieb joes:

Am Fri, 01 Nov 2024 18:03:26 +0100 schrieb WM:

>

If an invariable set of numbers is there, then there is a smallest
and a largest number of those which are existing.

or each and every n e IN there is an n' e IN (say n' = n+1)

Actual infinity is not based on claims for each and every, but concerns
all.

Lol. That actually sheds some light on your thought process:
how do you suppose some property holds for all x, but not
for every?

>
Every natnumber is finite. But here I mean that not only induction can
be applied and that induction is not valid for all natnumbers.
>
Regards, WM
>

>
But Induction *IS* valid for all Natural Numbers.
>
Or is your "natnumber" a code word for a number system that is supposed
to be like the Natural Numbers, but missing something so it isn't the
actual infinite number system it needs to be.

The universal quantifier can be dis-ambiguated
for-any for-each for-every for-all
because sometimes the comprehension implies things various,
like that deduction arrives at an infinitely-grand integer.
Then though it goes without saying
that all the perceived wrongs of thinking it wrong the one way
apply the other.
That's though a bit of rhetoric,
gently one would hope,
to help avoid the trap of hypocrisy.