Proofs

Title
1 plus 1 = 2
The square root of 2 isn't rational
Infinitely many prime numbers
Fundamental theorem of calculus
Prime decomposition
Metric spaces induce a topology
A convergent sequence of integers is eventually constant
Continuous positive functions on metric spaces
Axioms
A non-zero converging infinite sum has terms converging to 1
Integer multiplication is strictly increasing
Wave equation in two dimensions