How do we prove for $$S = \{ y \in \mathbb R | y^3 \leq x\}$$ $x$ is $\alpha^3$ for which $\alpha$ is the least upper bound of S? I try to rule out $\alpha^3 < x$ and $\alpha^3 > x$ but I have no idea how to prove? (Note: assume we do not know the existence of cube root)
2026-03-28 20:54:08.1774731248
Prove Least Upper Bound of a Set
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