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Apr 22, 2019 at 13:49 comment added Xander Henderson There are actually some notable inequalities (in English). For example, in functional analysis, there are the Cauchy-Schartz and Minkowski inequalities, as well as many Sobolev inequalities. Oh! and the Poincare inequality. That being said, there are vanishingly few important inequalities that appear before graduate school, so perhaps this is what is meant when you say that there are few inequalities which students routinely come across. I have upvoted this answer, by the way.
Apr 20, 2019 at 6:49 comment added Jessica B @BPP Also, I have never heard those other identities referred to as such. I'm not saying there are no other identities, only that we don't point them out as such so students very rarely hear the term in any other context.
Apr 20, 2019 at 6:47 comment added Jessica B @BPP I started writing a comment, but then realised what I was writing is an answer. The question is why we don't distinguish inequality and inequation. The answer is that we make so little distinction between equation and identity that there's not really a good reason to do so.
Apr 19, 2019 at 15:37 comment added user5402 That isn't an answer, it should be a comment.
Apr 19, 2019 at 15:37 comment added user5402 I've rarely seen an identity referred to as an equation; we call it a formula but not an equation. $(a+b)^2=a^2+b^2+2ab$ is an algebraic identity, $\left(u(x)v(x)\right)'=u'(x)v(x)+u(x)v'(x)$ ... Identities are everywhere not only in trigonometry.
Apr 19, 2019 at 7:24 history answered Jessica B CC BY-SA 4.0