Definition:Cut (Analysis)/Rational

Definition

Let $r \in \Q$ be a rational number.

Let $\alpha$ be the cut consisting of all rational numbers $p$ such that $p < r$.

Then $\alpha$ is referred to as a rational cut.

To express the fact that $\alpha$ is a rational cut, the notation $\alpha = r^*$ can be used.

Also see

• Rational Cut has Smallest Upper Number

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.7$. Definition