Definition
Suppose { fn } is a sequence of functions sharing the same domain and codomain (for the moment, we defer specifying the nature of the values of these functions, but the reader may take them to be real numbers). The sequence { fn } converges pointwise to f, often written as
if and only if
for every x in the domain.
Read more about this topic: Pointwise Convergence
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)