Continuity
A piecewise function is continuous on a given interval if the following conditions are met:
- it is defined throughout that interval
- its constituent functions are continuous on that interval
- there is no discontinuity at each endpoint of the subdomains within that interval.
The pictured function, for example, is piecewise continuous throughout its subdomains, but is not continuous on the entire domain. The pictured function contains a jump discontinuity at .
Read more about this topic: Piecewise
Famous quotes containing the word continuity:
“The dialectic between change and continuity is a painful but deeply instructive one, in personal life as in the life of a people. To “see the light” too often has meant rejecting the treasures found in darkness.”
—Adrienne Rich (b. 1929)
“Every society consists of men in the process of developing from children into parents. To assure continuity of tradition, society must early prepare for parenthood in its children; and it must take care of the unavoidable remnants of infantility in its adults. This is a large order, especially since a society needs many beings who can follow, a few who can lead, and some who can do both, alternately or in different areas of life.”
—Erik H. Erikson (1904–1994)
“Continuous eloquence wearies.... Grandeur must be abandoned to be appreciated. Continuity in everything is unpleasant. Cold is agreeable, that we may get warm.”
—Blaise Pascal (1623–1662)