whats the deal with this wacky theorem? i learned it in class and had a mild understanding of it, but i don't see the use in defining a limit like that.

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- Aug 9th 2008, 01:51 PMDubulusepsilon delta
whats the deal with this wacky theorem? i learned it in class and had a mild understanding of it, but i don't see the use in defining a limit like that.

- Aug 9th 2008, 02:16 PMo_O
It's not a wacky theorem. It's just a way of defining a limit. If you put some thought into it, the epsilon-delta definition of a limit makes a lot of sense.

- Aug 9th 2008, 02:35 PMgalactus
See here for a video on the subject.

YouTube - Calculus: Proof of a limit

I agree in that something that is rather intuitive is turned into a complicated sounding mess that can put new calc students off the subject. - Aug 10th 2008, 02:21 AMkalagota
- Aug 10th 2008, 10:56 AMDubulus
i was just kiddin around with the wacky theorem remark...but once you've defined it in that respect, what do you do with it? i went through all my calculus courses and i never heard of it until my advanced mathematics class. so if im not using the definition to actually learn what it is, whats the point?

- Aug 11th 2008, 02:50 AMkalagota
pointless.. and in fact, mathematicians are trying to work on spaces that will never exist such as $\displaystyle \mathbb{R}^n$ for $\displaystyle n\geq4$. and the question is, WHY?

...and, why do you stay as a math major knowing this situation?...

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anyways, since we are trying to study spaces (some of which never would exist), how would you explain that a "point" approaches another "point" along a function?*for me*, the easiest way to explain this is thru that epsilon-delta definition. since we were taught that this definition looks very much like our intuitive definition in one, two or three dimensional real-valued functions, it should be easily understood. (make sense? maybe..:) )

and if you asked me back why i stay as a math major, i'll answer "i just want to see and to appreciate the beauty of mathematics, aside from getting a degree and wanting to pass what i have learned, nothing so special.".... and i remember what my professors told us, "Learning mathematics(and when they say mathematics, they meant the broadest mathematics) should be a passion. If you only want money, you better shift out to another course."(i just want to share this..)