Editing Proof Let A, B be finite sets, and letf:A B be a function. Then: ii) If fis surjective, then 4| B| Proof: Let B-{b,, b2, b3, . . ., bm}, so B = m. Assume that f:A→B is onto and that B|> |4|. Since fis onto, for each i = 1, 2, ..., m we can find an %3D %3D element in A such that f(a) = b, Since B > LA|, there must exist some i + k, so that a, = a; = x, and so we would have f (x) = b, and also f(x) = b;. This is a contradiction, because it would mean that fis not really a function. Thus, we must have B < L4|

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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.