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

Am 15.09.2024 um 02:18 schrieb Chris M. Thomasson:

On 9/14/2024 5:07 PM, Moebius wrote:

Am 15.09.2024 um 01:54 schrieb Chris M. Thomasson:

On 9/14/2024 10:30 AM, FromTheRafters wrote:

WM presented the following explanation :

On 14.09.2024 01:05, FromTheRafters wrote:

WM explained :

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No, that is your big mistake. In the interval [0, 1] there is a point next to 0 and a point next to 1, and infinitely many are beteen them.

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Define 'next [to]' in this context.

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Two points are next to each other means that no point is between them.

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So which point is next to zero. Is it rational, or is it irrational? In either case it is greater than zero and there is again more room for an even closer number.

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If r e IR, r > 0, then 0 < r/2 < r.
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Hence there is no real number > 0 "next to 0".
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WM says .00001 is next to zero... Ahhh shit, what about .000001?

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.(0)1 is close to zero? ;^D

 Close, but no cigar.
 After all, 0.(0)01 is closer. :-P