2
votes
Accepted
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,...
- 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 ...
- 261
1
vote
Accepted
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 ...
- 6,275
1
vote
Accepted
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 ...
- 12.7k
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