Editing Asymptotic
You are currently browsing as guest..
To change this, fill in the following fields:
Username
Password
Click here to reset your password
Who can read this page?
The World
Members
Council
Admin
You have been granted an edit lock on this page
until Wed May 8 06:02:31 2024.
Press
to finish editing.
Who can edit this page?
World editing disabled
Members
Council
Admin
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.