# Inequality vs. Inequation, Equation vs. Equality

When talking about statements that two terms are mathematically (un-)equal (e.g., `1 = 1`, `1 < 2`, or `1 != 2`), what is the correct notion for such mathematical statements? Are there special cases w.r.t. "mixed" relations like `x <= y`? Can some notions be used interchangeably?

It seems many online sources use "equation" and "inequality" but there is also a Wikipedia page about "inequation". Apart from personal posts in forums, I have not found any sources using "equality" in such a situation, yet. Systematically, I would think that "equation" and "inequation" would make more sense than "equation" and "inequality", but not everything (probably very few things) in natural languages have developed according to a purely logical system.

Note that this question is more general than How to express the relationship that two numbers are not equal? for that it particularly asks for the relation between the notion for equations and the one for inequalities. Equations are not part of the existing question at all.

• I have never heard "inequation" used. It may be used in some math texts, but it is not "normal" English. If you want to avoid strange looks I'd recommend using "inequality", except perhaps in a context where you know "inequation" is accepted. Jan 21, 2016 at 0:49
• Possible duplicate of english.stackexchange.com/questions/292333/… Jan 21, 2016 at 1:34