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limit lim·it (lĭm'ĭt)
The point, edge, or line beyond which something cannot or may not proceed.
A confining or restricting object, agent, or influence.
The greatest or least amount, number, or extent allowed or possible.
To confine or restrict within a boundary or bounds.
To fix definitely; to specify.
A number or point for which, from a given set of numbers or points, one can choose an arbitrarily close number or point. For example, for the set of all real numbers greater than zero and less than one, the numbers one and zero are limit points, since one can pick a number from the set arbitrarily close to one or zero (even though one and zero are not themselves in the set). Limits form the basis for calculus, where a number L is defined to be the limit approached by a function f(x) as x approaches a if, for every positive number ε, there exists a number δ such that |f(x)-L| < ε if 0 < |x-a| < δ.