Heine Definition of ContinuityContinuity of Functions A real function f (x) is said to be continuous at ( is the set of real numbers), if for any sequence such that it holds that In practice, it is convenient to use the following three conditions of continuity of a function f (x) at point x = a: 1. Function f (x) is defined at x = a; 2. Limit exists; 3. It holds that . Cauchy Definition of Continuity ( - Definition) Consider a function f (x) that maps a set of real numbers to another set B of real numbers. The function f (x) is said to be continuous at if for any number there exists some number such that for all with the value of f (x) satisfies:
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