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

Cut property for real numbers

If $A$ and $B$ are nonempty, disjoint sets with $A \cup B = R$ and $a < b$ for all $a \in A$ and $a < b$ , then there exists a [...] such [...].

This a Dekekind cut and Dedekind completeness.

The cut property expresses the idea that sets of reals always have a boundary which is itself a real.

21.02.2021