Definition talk:Homomorphism (Abstract Algebra)

Is it modern convention to say something like $$\varphi(a)=a~\forall ~a\in F$$? If so I think I'm going to go and kill myself.

I learned to write it $$\forall a\in F: \varphi(a)=a$$ so as to emphasise the scope of the $$\forall$$. Otherwise (in more complicated constructions) the precise meaning of a nested sequence of $$\forall, \exists$$ etc. can become ambiguous. If the fundamentals of logic are no longer considered part of mathematical rigor then it's a disappointing development. --Matt Westwood 07:33, 20 December 2008 (UTC)

Ummm, "statement for all elements" and "for all elements, statement" seem the same to me, though were the statement to include "there exists" you wouldn't catch me dead commuting the two. Such is the difference between convergence and uniform convergence, continuity and uniform continuity, etc. What I've done here is fine given the context of the statement. --Grambottle 16:15, 20 December 2008 (UTC)