Definition:Cut (Analysis)/Upper Number

Definition

Let $\alpha$ be a cut.

Let $q \in \Q$ such that $q \notin \alpha$.

Then $p$ is referred to as an upper number of $\alpha$.

Also see

• Definition:Lower Number of Cut

• Rational Number Not in Cut is Greater than Element of Cut, where it is shown that if $q \notin \alpha$ then $\forall p \in \alpha: q > p$.

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.5$. Theorem