Migration complete - please let us know if anything isn't working.
One way of saying that two functions f(x) and g(x) are about the same size is to say that they are asymptotically equal: Two functions f(x) and g(x)are asymptotically equal (as x approaches infinity) if the following limit holds:
This is often denoted f(x)~ g(x).
For example: 3x4+2x+7 ~ 3x4, x+sin x ~ x, and the prime number theorem states that pi(x) ~ x/ln x.
If f(x)~g(x), then f is O(g) and g is O(f), but the converse is not true. Equivalently, if f(x)~ g(x), then g has the same order of magnitude as f (and again the converse is false). Finally, if f(x)~ g(x), then f(x)- g(x) is o(g(x)).
Printed from the PrimePages <t5k.org> © Reginald McLean.