Big O Magnitude Notation: Difference between revisions
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Created page with "Like Big O Unit Notation, Big O Magnitude Notation refers to a notation used to express orders of magnitude. == Formal Definition for Functions == A function <math>f(n) = O(10^k)</math> if <math>\exists n_0 \in \mathbb{R+}</math> such that <math>\forall n \geq n_0 : 10^k \leq f(n) < 10^{k+1}</math> == Formal Definition for Random Variables == Colloquially, one can say a random variable <math>X = O(10^k)</math> if its probability distribution function has meas..." |
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== Formal Definition for Functions == | == Formal Definition for Functions == | ||
A function <math>f(n) = O(10^k)</math> if <math>\exists n_0 \in \mathbb{R+}</math> such that <math>\forall n \geq n_0 : 10^k \leq f(n) < 10^{k+1}</math> | A function <math>f(n)=O(10^k)</math> for some fixed <math>k \in \mathbb{Z+}</math> if <math>\exists n_0 \in \mathbb{R+}</math> such that <math>\forall n \geq n_0 : 10^k \leq f(n) < 10^{k+1}</math> | ||
== Formal Definition for Random Variables == | == Formal Definition for Random Variables == | ||
A random variable <math>X = O(10^k)</math> if <math>P[10^k \leq X < 10^{k+1}] = 1</math>. | |||
[[Category:Concepts]] | |||
Latest revision as of 00:24, 29 August 2024
Like Big O Unit Notation, Big O Magnitude Notation refers to a notation used to express orders of magnitude.
Formal Definition for Functions[edit]
A function for some fixed if such that
Formal Definition for Random Variables[edit]
A random variable if .
![{\displaystyle P[10^{k}\leq X<10^{k+1}]=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/184ede8aea89ca2402e00ef5e7d473fe2eefe837)
