Category:Definitions/Cuts

This category contains definitions related to Cuts.
Related results can be found in Category:Cuts.

Let $\alpha \subset \Q$ be a subset of the set of rational numbers $\Q$ which has the following properties:

$(1): \quad \alpha \ne \O$ and $\alpha \ne \Q$, that is: $\alpha$ contains at least one rational number but not all rational numbers

$(2): \quad$ If $p \in \alpha$ and $q \in \Q$ such that $q < p$, then $q \in \alpha$

$(3): \quad \alpha$ does not contain a greatest element.

Then $\alpha$ is called a cut.