What does this order symbol mean?

[fedaykin]

As I can't seem to find a way to post an attachment, here's a link to a page with the symbol.
http://musr.phas.ubc.ca/symbols/
It is next to the text calO

One can see it in a context at http://en.wikipedia.org/wiki/R-parity
under the paragraph Proton Decay.

 

[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

 

[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.

 

[samspotting]

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

 

[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?