Big O Magnitude Notation

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 $f(n)=O(10^{k})$ if $\exists n_{0}\in \mathbb {R+}$ such that $\forall n\geq n_{0}:10^{k}\leq f(n)<10^{k+1}$

Formal Definition for Random Variables

Colloquially, one can say a random variable $X=O(10^{k})$ if its probability distribution function has measure zero outside of $[10^{k},10^{k+1}]$