Definition:Little-O Notation/Real/Infinity/Definition 1
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Definition
Let $f$ and $g$ be real functions defined on a neighborhood of $+ \infty$ in $\R$.
Let $\map g x \ne 0$ for $x$ sufficiently large.
$f$ is little-$\oo$ of $g$ as $x \to \infty$ if and only if:
- $\ds \lim_{x \mathop \to \infty} \frac {\map f x} {\map g x} = 0$
Also see
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 10.1$
- 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.6$ Some notations