Mathematics is about accepting fundamentals "truths" called axioms, and building a system with it. Depending of what axioms you want to use, you can prove 1 + 1 = 2. For example you can use the  Peano Axioms:

for addition:

    ∀n:n+0=n

∀n,m:n+s(m)=s(n+m)


And the definitions:

    1≡s(0)

2≡s(1)≡s(s(0))


We have:
1+1≡1+s(0)

=s(1+0) by axiom 2
=s(1)≡2 by axiom 1
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence