Here is a minimalist step-by-step proof with simple explanations that the square root of 2 is an irrational number. Thousands of years ago, Greek mathematicians discovered that there are irrational numbers. The following proof is a classic example of proof by contradiction. We will assume that our claim is not true, and then we will come to a contradiction. Since there are no contradictions in mathematics, we must accept that our claim is true.
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