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
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“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
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—Florence Nightingale (1820–1910)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)