Help Big-O proof troubles

Asked Sep 07 '17 at 14:20

Active Sep 07 '17 at 14:28

Viewed 32 times

I need to prove the rule that if $f(n) \in g(n) + O(h(n))$ then $g(n)\in f(n) + O(h(n))$

I have made several attempts but never get far as I'm not quite sure where to begin.

edited Sep 07 '17 at 14:28

Parcly Taxel

asked Sep 07 '17 at 14:20

S. Sav

1

What does E mean to you? – davidlowryduda Sep 07 '17 at 14:22
Should E represent $\in$? I.e. Do you mean that the rule is: if $f(n) \in g(n) + O(h(n))$ then $g(n) \in f(n) + O(h(n))$? – Mr Tsjolder from codidact Sep 07 '17 at 14:23
I think you mean that $f(n)-g(n) \in O(h(n)) \Rightarrow g(n)-f(n) \in O(h(n))$, which is basically automatic since the two left sides have the same magnitude in the first place. – Ian Sep 07 '17 at 14:30

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