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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Mon, 04 Nov 2024 06:10:41 -0500
Organization: Peripheral Visions
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WM presented the following explanation :
> 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.

"Only for all natnumbers which can be (weasel word) and which belong to 
a finite initial segment which is followed by ℵo natnumbers most of 
which you cannot (weasel word)."