Definition talk:Equation

Just what is an equation in a normal context? I think we need a workaday definition for a such a word that appears everywhere in mathematics.

So far I have seen that an equation is always of the form:

$f \left({x_1,...,x_n}\right) = g \left({x_{n+1},...,x_m}\right)$

and the solution set of an equation is the set of $m$-tuples such that the equation holds.

I think perhaps ProofWiki should be used with care. It makes one ask "But do I really know what that means?" constantly. --Jshflynn 13:44, 17 August 2012 (UTC)

As it should be. Symbolic statements about equality generally use the familiar $=$ symbol, but I'd rather not confine to an intuitive notion that involves functions on either side. This is of course how the stuff is used in analysis and its derivatives, but there's more to math than those fields... IMHO the definition currently up is just fine. --Lord_Farin 15:16, 17 August 2012 (UTC)

Regarding the solution set, though. Tarski says that the way equations are used, often there is an implied $\exists$ or $\forall$. Should I add that to the page? --GFauxPas 15:31, 17 August 2012 (UTC)

No. This page defines an equation. Discussing how it's used is the job of an encyclopedia. ProofWiki is a dictionary. --prime mover 17:01, 17 August 2012 (UTC)