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S(N) is just S(N), it's not N+1 unless you define it that way. S(0) is not 1, it's S(0). The successor function doesn't really get mapped to numbers without a
by empath75 2y ago
S(N) is just S(N), it's not N+1 unless you define it that way. S(0) is not 1, it's S(0). The successor function doesn't really get mapped to numbers without an explicit additional mapping.
- account42 2y agoUnless you are talking about an alternative number system where 1+1 is not 2 then yes, S(0) is 1.
- empath75 2y agoNo, it's not. That's just the standard model of peano arithmetic. You can map the successor function to many different operations and objects that aren't even numbers.
- account42 2y agoYes it is. "1" is just a label for what is also known as S(0) no mater what other ways you invent to refer to that element. Just like 一 is another label for the same concept.