The given statement is true. If n^2 is even, then n is even.
The proof that 0.999... = 1 is elementary, using just the mathematical tools of comparison and addition of (finite) decimal numbers.
The Euler's formula states that for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. This can be proven using the Noah's Ark method, which states that if you have a convex polyhedron with V vertices, E edges, and F faces, then V - E + F = 2.
This excerpt proves the Pythagoras' Theorem using Euclid's proof.
The Pythagorean Theorem states that the sum of the areas of the two small squares is equal to the area of the big one. In algebraic terms, this can be represented as a² + b² = c², where c is the hypotenuse and a and b are the legs of the triangle.
The Pythagorean Theorem states that the length of the diagonal of a square is equal to the square root of 2. This proof shows that the square root of 2 is irrational.