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From: Moebius
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Tue, 16 Jul 2024 03:39:26 +0200
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Am 16.07.2024 um 03:27 schrieb Chris M. Thomasson:
> Naturals:
>
> a = any natural number
> b = a + 1 is the /successor/ of a?
>
> ;^)
Hell, man, you are asking questions... :-)
Ok, starting with the Peano-axioms there is a functions called /the
successor function/ s. Then THE successor of, say, n is s(n). :-)
Based on the Peano-axioms we usually define "addition" + ("recursively")
the following way:
n + 0 = n
n + s(m) = s(n + m).
Moreover we (usually) have the definition:
1 := s(0).
"1 is the successor of 0".
Hence
n + 1 = n + s(0) = s(n + 0) = s(n).
So, yes, a + 1 is indeed the successor of a (for any a e IN).