# Definition:Cut (Analysis)/Rational

< Definition:Cut (Analysis)(Redirected from Definition:Rational Cut)

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## 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

## 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