## Proofs

##### Prove that if n^2 is even, then n is even.

The given statement is true. If n^2 is even, then n is even.

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##### A proof that 0.999... = 1

The proof that 0.999... = 1 is elementary, using just the mathematical tools of comparison and addition of (finite) decimal numbers.

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##### Euler's formula

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.

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##### Euclid's Proof of the Pythagorean Theorem

This excerpt proves the Pythagoras' Theorem using Euclid's proof.

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##### Proof that square root of 2 is irrational.

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.

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