Thank you for this. It doesn’t exactly help regarding my reasoning but I think your method is easier to prove that f is O(g). I didn’t know about it so thanks for introducing it to me^
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There's a much more succinct and formal way of putting what I think your reasoning is:
if the limit of f(n) / g(n) is a finite number as n goes to infinity, then f is O(g).
So for example, if you're comparing
3𝑛³ + 2n²to5𝑛³, the limit of the ratio is3/5, which is a finite number, so3𝑛³ + 2n²isO(5𝑛³).On the other hand, if we compare
10n²andn, the limit is +infinity. So that means10n²is NOTO(n).Thank you for this. It doesn’t exactly help regarding my reasoning but I think your method is easier to prove that f is O(g). I didn’t know about it so thanks for introducing it to me^