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continuity |
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continuityIn mathematics, a property of functions and their graphs. A continuous function is one whose graph has no breaks, gaps, or jumps. It is defined using the concept of a limit. Specifically, a function is said to be continuous at a value x if the limit of the function exists there and is equal to the function's value at that point. When this condition holds true for all real number values of x in an interval, the result is a graph that can be drawn over that interval without lifting the pencil. Such functions are crucial to the theory of calculus, not just because they model most physical systems but because the theorems that lead to the derivative and the integral assume the continuity of the functions involved. |
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| In this ceaseless rush of shadows and shades, that, like the fantastic forms of clouds cast darkly upon the waters on a windy day, fly past us to fall headlong below the hard edge of an implacable horizon, we must turn to the national spirit, which, superior in its force and continuity to good and evil fortune, can alone give us the feeling of an enduring existence and of an invincible power against the fates. But the hypothesis of continuity in mental development is clearly preferable if no psychological facts make it impossible. With respect to a tyranny he neither says whether there will be any change in it; or if not, to what cause it will be owing; or if there is, into what other state it will alter: but the reason of this is, that a tyranny is an indeterminate government; and, according to him, every state ought to alter into the first, and most perfect, thus the continuity and circle would be preserved. |
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continuity
