The question in question asks whether the AM-GM inequality can be, in some sense, reduced to the case where there is equality. I think this is a reasonable question, and here is a proposed plan for an answer: one could outline a proof for the inequality, in which one brings two variables together, and shows that this decreases the GM without changing the AM; after finitely many such operations, we are left with the case of equality.
The OP also recently asked another contentious question, which doesn't make much sense to me, and was promptly closed. A possible different course of action, which might be less alienating, is to ask the OP to explain his motives better.
:)
And it is better to click the green check mark after either (a) question is re-opened or (b) the community decides it shouldn't be re-opened. $\endgroup$ – Willie Wong Apr 30 '11 at 0:42