big O notation (Q269878)

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notation to describe the limiting behavior of a function
  • Landau notation
  • Bachmann–Landau notation
  • asymptotic notation
  • Landau symbol
  • order comparable with or inferior to
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Language Label Description Also known as
English
big O notation
notation to describe the limiting behavior of a function
  • Landau notation
  • Bachmann–Landau notation
  • asymptotic notation
  • Landau symbol
  • order comparable with or inferior to

Statements

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Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle f(x)=\operatorname {O} (g(x)){\text{ as }}x\rightarrow \infty \iff \exists M>0,x\in \mathbb {R} :|f(x)|\leq Mg(x),\quad \forall x\geq x_{0}}
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. upstream connect error or disconnect/reset before headers. reset reason: connection failure"): {\displaystyle f(x)=\operatorname {O} (g(x)){\text{ as }}x\rightarrow a\iff \limsup _{n\rightarrow a}{\frac {|f(n)|}{g(n)}}<\infty }
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. upstream connect error or disconnect/reset before headers. reset reason: connection failure"): {\displaystyle f(x)=\operatorname {O} (g(x))}
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