Definition
Formally, given complex-valued functions f and g of a natural number variable n, one writes
to express the fact, stated terms of little-o notation, that
or equivalently
Explicitly this means that for every positive constant ε there exists a constant N such that
- .
Unless g(n) is infinitely often zero (which would make the limit below undefined), this statement is also equivalent to
This relation is an equivalence relation on the set of functions of n. The equivalence class of f informally consists of all functions g which are approximately equal to f in a relative sense, in the limit.
Read more about this topic: Asymptotic Analysis
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—George Eliot [Mary Ann (or Marian)
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Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
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—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)