I am in a real analysis class and am having difficulty with this problem:
prove that any non negative real number has a square root.
2026-04-08 15:00:09.1775660409
Prove that any non negative number has a square root
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Let $b>0$ and consider the set given by: $$S_b=\{x\in\mathbb{R}:x^2<b\}.$$ Then prove that this set has an upper bound, and that $\alpha=\sup S_b$ satisfies $\alpha^2=b$