Hi, i was reading an online course about asymptotic analysis in which its mentioned that o(10^n) belongs to o(nlogn). By definition of little o, a function f(n) belongs to g(n), if for all n > n0(some positive value) and c > 0 f(n) < cg(n). Can some please explain how 10^n is less than nlogn ?

I don’t think it is. The definition provided in the following link says it all.

https://xlinux.nist.gov/dads/HTML/littleOnotation.html

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Here’s where you got it wrong.

n + 10 \in o(n^2) \in o(10^n) \in o(n\log{n})\ \cancel{\in}\ o(n)\ \cancel{\in}\ o(n - 10) implies

n + 10 \in O(n^2) and

n + 10 \in O(10^n) and

n + 10 \in O(n\log{n})

Which doesn’t imply 10^n = o(n\log{n}) !!!

It seems the course has misleading content.

Okay, thanks!!