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Math and science::Analysis::Tao::05. The real numbers

Least upper bound

Let \( E \) be a subset of \( \mathbb{R} \) and let \( M \) be a real number. We say that \( M \) is a least upper bound for E iff:
  1. \( M \) is an [...] for \( E \).
  2. Any other upper bound for \( E \) is [...].