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From: Ben Bacarisse <ben@bsb.me.uk>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Mon, 16 Sep 2024 22:47:37 +0100
Organization: A noiseless patient Spider
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Ross Finlayson <ross.a.finlayson@gmail.com> writes:

> On 09/15/2024 09:38 AM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> On 9/14/2024 11:35 AM, joes wrote:
>>>> Am Sat, 14 Sep 2024 16:01:02 +0200 schrieb WM:
>>>>> On 14.09.2024 01:05, FromTheRafters wrote:
>>>>>> WM explained :
>>>>>
>>>>>>> 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.
>>>>>> Define 'next' in this context.
>>>>> Two points are next to each other means that no point is between them.
>>>> Which is the case for no two (different) reals.
>>>
>>> Two points on the real line that are different from one another have
>>> infinite points between them, and so on and so forth. :^)
>>
>> It might be worth pointing out that any non-trivial interval [a, b] on
>> the real line (i.e. with b > a) contains an uncountable number of
>> points.  Constructing the mid point and the quarter points and so on
>> only shows a countably infinite number of internal points, but giving a
>> bijection between [a, b] and [0, 1] shows that they have the same
>> cardinality.
>
> Perhaps you might care to define "function" and "topology".

Do you not have any good textbooks?

-- 
Ben.