# Confused on Little Oh

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I was reading the Little Oh notation in a textbook. Apparently it has two meanings:

1) f(x) is Big-Oh (gx)  which means f(x) <= g(x)

2) f(x) is NOT Big-Theta g(x)^4. (This definition confused me a lot.)

In my own words this would mean: f(x) <= g(x). Since Big Theta is Big Oh and Big Omega combined. f(x) is NOT <= g(x)^4 would mean f(x) is > g(x)^4 and f(x) is NOT >= g(x)^4 which mean f(x) is < g(x) ^ 4. Based on what I said, wouldn't the second definition actually mean f(x) is Big Theta g(x)^4?

Please correct me if I'm wrong.

Edited by warnexus

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I don't know about your second question, but the first statement where you rephrased f(x) = o(g(x)) into your own words is a bit off. f(x) < g(x) for all x. Not <=. f(x) is inferiorly less than g(x) for all x. That's the definition of little-oh.

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Thanks Steve for the correct definition. It is much easier to remember.

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Your question is impossible for me to comprehend.  Little O has a very precise meaning.

http://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann.E2.80.93Landau_notations

The key difference between Big O and Little O is that there's some notion of bounds tightness in Big O that is not necessary for Little O.