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

On 07.11.2024 03:27, Richard Damon wrote:

On 11/6/24 10:15 AM, WM wrote:

On 06.11.2024 12:46, Richard Damon wrote:

On 11/5/24 11:45 AM, WM wrote:

On 05.11.2024 04:08, Richard Damon wrote:

On 11/4/24 12:11 PM, WM wrote:

On 04.11.2024 13:14, Richard Damon wrote:

On 11/4/24 6:07 AM, WM wrote:

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By induction you can prove the sum n(n+1)/2 for every initial segment 1+2+3+...+n. But not for all natural numbers.

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But all Natural Numbers can be defined.

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All defined numbers can be summed. Not all natural numbers can be summed.

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Why not?

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because most cannot be defined.

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But they ARE defined.

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Then sum all of them.

They will sum to Aleph_0

That is not a sum. It is just another name for infinity.

Note, Addition on Natural Numbers is closed for FINITE sums (the sum of a finite number of numbers), not necessarily for infinite series of them.

That is because infinitely many always contain dark numbers. All not dark numbers can be summed.
Regards, WM