## Most recent change of Asymptotic

Edit made on February 21, 2009 by RiderOfGiraffes at 13:25:41

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Suppose /f/ and /g/ are two functions, and we are interested in what happens to EQN:f(x) and EQN:g(x) as /x/ grows. We say that " /f/ is asymptotic to /g/ ", or EQN:f\sim~g, if their ratio tends to 1. For instance, EQN:x^2+5x-\log~x\sim~x^2, and (more interestingly and much less obviously) EQN:\pi(x)\sim\text{Li}(x) where EQN:\pi is the prime counting function and Li is the logarithmic integral.

Suppose /f/ and /g/ are two functions, and we are interested in what happens to

EQN:f(x) and EQN:g(x) as /x/ grows. We say that " /f/ is asymptotic to /g/ ", or

EQN:f\sim~g, if their ratio tends to 1. For instance, EQN:x^2+5x-\log~x\sim~x^2,

and (more interestingly and much less obviously) EQN:\pi(x)\sim\text{Li}(x) where

EQN:\pi is the prime counting function and Li is the logarithmic integral.

This last is the Prime Number Theorem.