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  Limit, in mathematics, is the concept which provides the essential basis for the study of analysis. The precise definition of the limit by Karl Weierstrass (1815 - 1897) was the breakthrough which enabled mathematicians to make the calculus rigorous in the 19th century, to establish it on an equal footing with other branches of mathematics. Weierstrass\'s definition of the limit amounted to the following. Suppose f is a function and a a point; the limit of f at a is L if for each non-zero epsilon there is a non-zero delta such that if x is less than delta away from a then f(x) is less than epsilon away from L. This rather complicated definition amounts (roughly) to saying that the closer x is to a, the closer f(x) is to L. SMcL  



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