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

On 11/4/2024 12:35 AM, FromTheRafters wrote:

Chris M. Thomasson submitted this idea :

On 11/3/2024 6:34 AM, joes wrote:

Am Sat, 02 Nov 2024 22:39:36 +0100 schrieb WM:

On 02.11.2024 21:34, Richard Damon wrote:

On 11/2/24 1:42 PM, WM wrote:

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.

But if it applies to ALL, it must apply to ANY, so a property of ANY
must apply to each on of the ALL.
So, for ALL the Natural Numbers, there can't be a highest, because for
ANY Natural Number there is a following one

That cannot be true for all dark numbers.

And that is why "dark" numbers are not natural (or the naturals are all
not dark).
>

>
Well, what if the dark numbers are natural wrt:
>
1, 2, 3, 4, ...
>
Oh shit! WM says ... is dark. I say 5, then WM says well okay 5 is not dark now. Shit like that? Its rather hilarious to me.

 It may make more sense to go higher. Consider the 123^456^789th prime number. I would be pairing the natural number 123^456^789 with some really large prime number. Which prime? I don't know. WM eschews such a pairing because the value of that prime is unknown, or 'dark' and he thinks it cannot be used in a pairing.

Cantor pairing can handle it it can take two primes and map them to a unique unsigned integer. Then it can go back from the result to the original two primes. WM ways, oh well, no it can't. It's just too god damn dark around here! ;^o

 Had I been matching instead of pairing, he would have a point because it would likely be impossible for me to check that the 123^456^789th prime has the correct natural number index. For pairing, I don't need the values, only the countability, but for matching I might.