# What does this order symbol mean?

1. Jan 3, 2009

### fedaykin

Last edited by a moderator: Apr 24, 2017
2. Jan 3, 2009

### Mute

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

3. Jan 3, 2009

### HallsofIvy

That is "on the order of". Its most general mathematics definition can be complicated but in this application saying "O(1)" really means "a few": less than 10 but more than 0.1. Saying that the lifetime of a proton is "O(1032) years" means that the lifetime of a proton is certainly greater than 1031 years but less than 1033 years.

Last edited by a moderator: Jan 5, 2009
4. Jan 3, 2009

5. Jan 3, 2009

### fedaykin

Thank you oh so very very much. I've noticed that there are letters that take a similar tex bitmap name; are they related?