8. If A is not totally bounded, show that A has an infinite subset B that is homeo- morphic to a discrete space (where B is supplied with its relative metric). [Hint: Find ɛ > 0 and a sequence (x,) in A such that d(xn, Xm) Z ɛ for n m. How does this help?]

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.