2 votes

Is my understanding of Peano Axioms as mentioned below correct? I’ll also be grateful if questions below are answered definitively

Speaking a bit imprecisely here, but here goes… Yes, the zero and successor function have no inherent meaning, except what is defined in the axioms. Yes Yes, the name of a function doesn't matter. No,...
ShyPerson's user avatar
  • 1,680
1 vote

Why universal closure?

If we want to talk about existentially quantified things, we often want to refer to them by name, so it's usually a good idea to name them by Skolemizing: instead of $∃x.P(x)$ introduce a constant ...
Alex's user avatar
  • 261
1 vote

What is 'increment' in Peano Axioms?

With Axiom1 & Axiom2 , we have to take $n++$ to indicate some "Successor" Natural Number , not necessarily the "Next" Natural Number. Here , $0++$ might be the Next Natural ...
Prem's user avatar
  • 6,275
1 vote

Are the axioms of analysis a combination of Peano axioms and set theory axioms?

An axiom is a statement that we assume to be true. Often it is added: "without proof". That's true in some way, but also misleading in some situations. For most modern mathematicians, the ...
Vercassivelaunos's user avatar

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