Definition: A function f: A --> R is continuous at a point c Element A if, for a

Question

Definition: A function f: A --> R is continuous at a point c Element A if, for all epsilon > 0, there exists delta > 0 such that whenever |x - c| < delta (and x Element A) it follows that |f(x) - f(c)| < epsilon. If f is continuous at every point in the domain of A, then we say that f is continuous on A. Explain how to take the logical negation of the precise definition of continuity. Explain what this statement means in plain English. How would you explain the concept of continuity to someone who has not studied advanced math?

Explanation / Answer

a function is said to be continuous if there is no large sudden change in value of f(x) at a point x and its neighbourhood.

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