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From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sat, 19 Oct 2024 18:22:54 -0000 (UTC)
Organization: muc.de e.V.
Message-ID: <vf0tdu$2fe9$2@news.muc.de>
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WM <wolfgang.mueckenheim@tha.de> wrote:
> On 19.10.2024 19:32, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:

>>> When multiplying all natural numbers by 2, then the number of numbers
>>> remains the same but the density is reduced and therefore the interval
>>> is doubled.

>> That's not mathematics.

> It is mathematics.

>> It's merely your intuition, derived from finite sets and misapplied to
>> infinite sets.

> It is the basic mathematics of natural numbers: 2n > n.

Of course 2n > n for all n > 0.  That has no connection with the other
crazy things you've been asserting.

> If you believe in a different version of mathematics, try to find
> people who are interested in that version.  I am not. 

The other posters on this newsgroups, they are not hard to find.  We all
understand standard mathematics.  You do not.

>> In mathematics, there is no meaningful distinction between what you think
>> of as two different forms of infinity.

> You have not the faintest idea of infinity.

But I do.  An infinite set is one which has a proper subset which can be
put into 1-1 correspondence with the original set.  That is the
definition.  You clearly don't understand that definition, and you go to
great lengths to preserve that lack of understanding.

> Regards, WM

-- 
Alan Mackenzie (Nuremberg, Germany).