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definition: Dom(f, g) : ∀n ∈ N, g(n) ≤ f(n). Let f(n) = n^2

and g(n) = n + 165. Prove that g is not dominated by f. so the negation for this question is...

∃n ∈ N, n + 165 > n^2

would you just give an example so when n =0 so.. 165>0

and you are done? Or am I misunderstanding?

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    An example of $\;n+165>n^2\;$ ? There are many, for example with $\;n=1,\,2,\,3,...,13\;$ , yet for $\;n=14\;$ we already have $\;14+165=179\color{red}<14^2=196\;$ ... – 2017-02-08
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    Yes, you just need to give an example $m$ where $f(m) – 2017-02-08
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    n=0 works also right? as 0 is natural... why did donantonio pick 14? just to illustrate one example? I don't understand the "we already have" maybe. – 2017-02-08
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    @shibu (1) Zero being a natural is a matter of agreement and, sometimes, even of bitter discussion: some consider it a natural, some don't. (2) It isn't clear from your question (poorly worded and written without MathJaX), but *if you need* to prove $\;f\;$ doesn't dominate $\;g\;$ , then yes: one single example makes the trick, so any one of the numbers I wrote in my first comment do it. – 2017-02-08

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