# What does this order symbol mean?

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Mute
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It means "Order" as in "order of magnitude". $\mathcal{O}(1)$, when referring to some quantity, means that the order of magnitude of the quantity is on the order of the number 1 - it's larger than 0.1 and less than 10. Typically we take order of things as powers of some number.

e.g. $x \sim \mathcal{O}(\lambda^n)$ means the variable x is of the same order of size as the parameter $\lambda$ to the nth power - it's between $\lambda^{n-1}$ and $\lambda^{n+1}$ in size.

See http://en.wikipedia.org/wiki/Big_O_notation

HallsofIvy