What does this order symbol mean?

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  • #2
Mute
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It means "Order" as in "order of magnitude". [itex]\mathcal{O}(1)[/itex], 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. [itex]x \sim \mathcal{O}(\lambda^n)[/itex] means the variable x is of the same order of size as the parameter [itex]\lambda[/itex] to the nth power - it's between [itex]\lambda^{n-1}[/itex] and [itex]\lambda^{n+1}[/itex] in size.

See http://en.wikipedia.org/wiki/Big_O_notation
 
  • #3
HallsofIvy
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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.
 
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  • #5
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Thank you oh so very very much. I've noticed that there are letters that take a similar tex bitmap name; are they related?
 

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