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

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

About this solution: This solution is correct and demonstrates a level of completeness. The approach is straightforward and uses only the mathematical tools of comparison and addition of decimal numbers.

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.

About this solution: The candidate's solution is correct and demonstrates a good understanding of the problem. The candidate has taken a clear and logical approach to solving the problem.