nLab denial inequality



Equality and Equivalence


The denial inequality is the negation of equality.

This is a term found in constructive mathematics, to distinguish from other inequality relations such as apartness. It is taken for granted in classical mathematics.

If one wishes to reserve the word “inequality” for order relations (such as \le and <\lt), then one may instead use the word disequality to refer to the denial inequality. (For instance, this is common in type theory with subtype relations that form an ordering on the types.)

Last revised on May 22, 2022 at 00:55:18. See the history of this page for a list of all contributions to it.