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

Chris M. Thomasson wrote :

On 10/10/2024 6:38 PM, Richard Damon wrote:

On 10/10/24 2:32 PM, WM wrote:

On 09.10.2024 21:13, Alan Mackenzie wrote:

WM <invalid@no.org> wrote:

Am 09.10.2024 um 18:12 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

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You've misunderstood the nature of N.  The set is not
{1, 2, 3, ..., ω}, it is {1, 2, 3, ...}.

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I use ℕ U {ω} for clarity.

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You would do better not to do so.  It gives wrong results.

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It gives unfamiliar results because you have no clear picture of actual infinity. If all natnumbers are there and if 2n is greater than n, then the doubled numbers do not fit into ℕ. But note, that is only true if all natnumbers do exist.

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No, *YOU* don't understand what actual infinity is like as you picture it just like the finite, but bigger.
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If not all do exist, te doubling yields larger natnumbers, some of which have not existed before. But that means potential infinity.

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But there aren't any natural numbers that have not existed before. That is just showing that your "actual infinity" is a finite set that you grabbed on the way to infinity, but didn't get there yet.
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Actual infinity means you need to wait until you get there. The problem is finite creatures can't do that, so can't handle actual infinity.

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What do you mean? I can say all the natural numbers. That was pretty fast for all of them. ;^)

 That's right, and we have no real need for an infinity which isn't infinite.