Little-o notation is a notation representing the behavior of a limit of a function at a given value. The statement

f(x) = o(g(x)) \, \, \, \text{as} \, \, \, x \to a

can be intuitively interpreted as saying that g(x) grows much faster than f(x) at a, or, more mathematically,

\lim_{x \to a} \frac{f(x)}{g(x)} = 0

Or, in cases where there is a third function, h(x):

f(x) = h(x) + o(g(x)) \Rarr \lim_{x \to a} \frac{f(x) - h(x)}{g(x)} = 0

For example:

  • x = o(x^2) \, \, \forall x
  • x^2 \neq o(x^2) \, \, \forall x
  • \sin(x) \neq o(x), x \rarr 0
  • \sin(x) \neq o(x^2), x \rarr 0
  • \sqrt{x} = \sqrt{3} + o(1), x \rarr 3

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