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Your Text: Insert Slimies » Insert UBB Code » Close Last Tag \| All Tags UBB Help	I am to write a plain-text essay on delta-epsilon; proofs for Calculus I, as some sort of cross-disciplinary testing my university is doing. Or whatever. The point is that I realized my knowledge of the Cauchy criterion is quite limited and has come to a halt due to a probably stupid misunderstanding! So here is what I have in outline. My gap in understanding is how the relationship between d [=delta] and e [=epsilon] is established. Also, to prove in the general case; I want to have command of the proof, because things get very muddy when dealing with complex transcendental functions and their δ-ε proofs. So I am talking it through and would appreciate some help. Besides, it's math. And everybody likes math. Ae>0 Ed>0 \| o<\|x-a\|<d --> \|f(x)-L\|<e where [lim x->a] f(x) = L So my d value must be substantially close such that no critical points exist between \|x-a\| which could disrupt the continuity of f(x). So my corresponding e is going to be some value defined by the criterion of d = (a-d, a)U(a, a+d) which will create corresponding points if f(x) is continuous at (L-e, e)U(e, L+e). The last part of the argument states: 0<\|x-a\|<d --> \|?(x)-L\|<e which means to me, and this is my point of [b]confusion[/i], that I want to define d according to the above restrictions and discover if a corresponding e exists. So following the rules of implication, the only way this statement would be true and the limit false is if 0<\|x-a\|<d is true and \|?(x)-L\|<e is false. [b]So how do I establish a relationship between d and e in the form of an equation, or do I need to do this?[/b] I know what I want to do, I just don't know how I need to do it. [EDIT: GRR. How do I represent mathematical symbols?] [EDIT: there we go.] [small](Edited by [url=http://www.ozoneasylum.com/user/4153]cfb[/url] on 04-11-2007 00:41)[/small] Loading...
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