Definition:Positive Cut

Definition

Let $\alpha$ be a cut.

Let $0^*$ be the rational cut associated with the (rational) number $0$.

Let $\alpha \ge 0^*$.

Then $\alpha$ can be referred to as a positive cut.

Strictly Positive Cut

Let $\alpha > 0^*$.

Then $\alpha$ can be referred to as a strictly positive cut.

Also known as

What $\mathsf{Pr} \infty \mathsf{fWiki}$ defines as a positive cut is referred to by some sources as a non-negative cut.

Such sources call a positive cut what $\mathsf{Pr} \infty \mathsf{fWiki}$ refer to as a strictly positive cut.

Also see

• Definition:Negative Cut
• Definition:Strictly Negative Cut

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Dedekind Cuts: $1.9$. Definition