What is the basis for the universe

>They use it, yes.
Who are "they" and what is "it"?

Can you demonstrate how 1+1=2 implies the Peano axioms?

Anyone trying to make a condtruction of the natural numbers.
That wasn't the point, the pibt is that in any model of the peano axioms, or some equivalent axiomatic system you either take that 1+1=2 or you need an equivalent axiom. In general it's not just 1+1=2, but a succesor function defining addition.

All of this is because some retard said that the proof of all vector spaces have a basis is not a proof, because it's equivalent to AC.

>That wasn't the point, the pibt is that in any model of the peano axioms, or some equivalent axiomatic system you either take that 1+1=2 or you need an equivalent axiom.
Now were just back to my original question which remains unanswered: Why do all proofs of 1+1=2 rely on an axiom equivalent to 1+1=2?

> the proof of all vector spaces have a basis is not a proof, because it's equivalent to AC.
This is true.

Because if we take peano axioms as a model of natural numbers, all other axiomatic systems for the natural numbers should give you the sane results. Because the existabce if a successor function is independent of the other aximos in Peanos formulation, if you want an equivalent AS, that gives you the same results as Peano, and you take out the succesor function axiom, you need set of statements equivalent to it, otherwise you may ebd with more or less true proofs.
So the proof of the well ordering principle is not a proof? You understand that you can't determine if two statements are equivalent a priori right? Zermeli still had to show the implication.

>Because if we take peano axioms as a model of natural numbers, all other axiomatic systems for the natural numbers should give you the sane results. Because the existabce if a successor function is independent of the other aximos in Peanos formulation, if you want an equivalent AS, that gives you the same results as Peano, and you take out the succesor function axiom, you need set of statements equivalent to it, otherwise you may ebd with more or less true proofs.
You're still not addressing my question, so to be more specific, which axiom is equivalent to 1+1=2?

If you don't know shit about logic I can't explain further. The point is not to give a specific Axiomatic system equivalent to Peano, but that all of them either contain the succesor function axiom or a statement equivalent to th

Equivalent to it. *

>If you don't know shit about logic I can't explain further. The point is not to give a specific Axiomatic system equivalent to Peano, but that all of them either contain the succesor function axiom or a statement equivalent to th
What part of my question do you not understand? You claimed "all proofs that 1+1=2 ... rely on axiom equivalent to 1+1=2". Which axiom is equivalent to 1+1=2?