Re: Does the number of nines increase?

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).