# Asymptotic Notation (Ex 3-4(h))

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Let $f(n)$ and $g(n)$ be asymptotically positive functions. Prove or disprove below fact

(h) $f(n)+o(f(n))=\Theta(f(n))$

is it true?
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what is h?
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where is h?
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ok sorry,

it is not correct I think

$f(n)+o(f(n))=O(f(n))$
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why ?

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difference between small-o and Big-O is a '='

f(n) is exact value here

and it brings '=' sign in the equation

so it converted to big-O
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Let f(n) be n, then o(f(n)) is > f(n). So let it be n2.

f(n) + o(f(n)) = c1*n + c2*n2 = ⊝(n2) ≠ ⊝(n) i.e. ⊝(f(n))

So I think it should be false.

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@srestha, @MiNiPanda,

Your Explanations satisfies me....

## 1 Answer

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I Think this statement is true, we can prove this using properties of asymptotic notation

Let me know if am wrong.

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