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

Am Thu, 03 Oct 2024 20:25:07 +0200 schrieb WM:

On 02.10.2024 22:07, Jim Burns wrote:

On 10/2/2024 7:12 AM, WM wrote:

On 01.10.2024 22:05, Jim Burns wrote:

 

For every nonzero distance d from 0 there are ℵ₀.many unit.fractions
closer than d

That means there is no d by what you can distinguish ℵ₀ unit
fractions?

You (WM) require us to guess what you mean by 'distinguish'.

You distinguish two unit fractions 1/n and 1/m if you place a point in
distance d from 0 between them: 1/n < d < 1/m.

Which is always possible.

There is no d between ℵ₀.many.smaller.unit.fractions and
slightly.fewer.than.ℵ₀.many.smaller.unit.fractions.

That means you cannot distinguish ℵ₀ smaller unit fractions.

Misconception: there is no „slightly fewer than ℵ₀”. An finite
number subtracted from an infinite is still the same infinite
number.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.