A bit of everything

# Proofs

Title
1 plus 1 = 2
The square root of 2 is not 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
Polynomials are smooth
The preimage theorem
Inequality of the power of a sum and the sum of the power
Gram-Schmidt process for Lorentzian spaces
Polar decomposition of Lorentz transforms
There exists a Lorentz transform between any two unit vector
Any two Lorentz space orthonormal basis are related by a Lorentz transform
For a positive definite metric if the triangle inequality is an equality the two vectors are colinear of same direction
The inner product of two collinear vectors is the product of their norms
Two timelike vectors can be put in a two-dimensional timelike subspace
Any vector can be decomposed into one vector and another in its orthogonal complement
If the integral of a locally bounded function is zero for all domains it is zero
The product of square integrable functions is the space of square integrable functions on the product
The flow-box theorem
Asymptotic expansion of the inverse of sums of matrices
Derivative of the determinant
Universal property of the empty set
Universal property of the product
Pullback bundle is a bundle