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Continuity - Definition
Intuitively, a curve y = f(x) is continuous if it forms an unbroken line, that is, whenever x1 is close to x2, f(x1) is close to f(x2). To make this intuitive idea into a mathematical definition, we substitute "infinitely close" for "close." DEFINITION f is said to be continuous at a point c if: (i) f is defined at c; (ii) whenever x is infinitely close to c, f(x) is infinitely close to f(c). If f is not continuous at c it is said to be discontinuous at c.
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Last Update: 2006-11-25