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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Mon, 4 Nov 2024 12:07:35 +0100
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On 03.11.2024 22:21, Richard Damon wrote:

> But Induction *IS* valid for all Natural Numbers.

Only for all natnumbers which can be defined and which belong to a 
finite initial segment which is followed by ℵo natnumbers most of which 
you cannot define.

By induction you can prove the sum n(n+1)/2 for every initial segment 
1+2+3+...+n. But not for all natural numbers.

Regards, WM