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.
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.
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?
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..)