If $A$ is a subset of the integers $\mathbb{Z}$, and is bounded above, then A has a supremum $\alpha$ that is an element of the integers $\mathbb{Z}$. Is this statement true?
2026-03-31 23:54:15.1775001255
Axiom of Completeness for set of integers
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It is not true. A counterexample is $A=\varnothing$, which is bounded above by $42$, but has no supremum in $\mathbb Z$.