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

On 10/8/2024 5:35 AM, Richard Damon wrote:

On 10/8/24 5:54 AM, WM wrote:

On 07.10.2024 15:19, Alan Mackenzie wrote:

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

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No, even an unbounded sequence does not get longer when shifted by one step.

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The concept of "length" appropriate for finite sets doesn't apply to
infinite sets.

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It is the concept of number of elements. It is appropriate in actual infinity.

 Which has been shown to not exist for us finite beings, as it is too big for us to see.
 

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infinite means "without end" - unendlich.

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Actual infinity means complete. That implies a fixed number.

 Which has been shown to not exist for us finite beings, as it is too big for us to see.
 

You don't understand that actual infinity is a fixed quantity.

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It may be "fixed" whatever that might mean, but to regard it as a
"quantity" is more than questionable.

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Fixed means that no element can be added and no element can be lost. The number of nines is fixed. That is an assumption only, but necessary for bijections.

 Yes, it is fixed, at INFINITY, which means there is no end to it, and thus we can't add a zero "at the end" which doesn't exist.
 This is why finite beings can't use "actual infinity" because it is too big for us to handle.

Ummm... Well, not sure what to think about that. Hummm... Any time you use a number it is in actual infinity. Think of the number four. It is in a pool of the infinitely many natural numbers, and we just used it...
Fair enough, or weasel words?