单词 | continuity |
释义 | continuity The absence of sudden jumps in a function. A function y = f(x) is continuous if as x changes by arbitrarily small amounts there are no sudden changes in y. Some functions are continuous for all values of x, for example y = x2. Other functions are continuous except at particular values of x. The function y = 1/x, for example, is continuous except at x = 0: as x approaches 0 from above, y becomes indefinitely large; as x approaches 0 from below, y becomes indefinitely large and negative; and for x = 0, y is not defined. In commonsense terms, y is a continuous function of x if its graph, with x and y on the axes, can be drawn without removing one's pen from the paper. |
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