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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 14 Jun 2024 23:01:39 -0700
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On 5/2/2024 10:06 AM, Moebius wrote:
> Am 30.04.2024 um 14:56 schrieb WM:
> 
>> The end is smaller than ω.
> 
> The sequence of natural numbers (all of which are smaller than ω) does 
> not have an end, Du Depp!
> 

Fwiw, here how I generally write my recursive functions. Say the natural 
numbers, including zero here:

r[0] = 0
r[n + 1] = r[n] + 1

Lets expand that for a couple of iterations:

r[0] = 0
r[1] = r[0] + 1 = 1
r[2] = r[1] + 1 = 2
r[3] = r[2] + 1 = 3
....

[n] where n is an index

vs:

r_0 = 0
r_(n+1) = r_n + 1

Both seem okay to me, as in I can understand both of them.