Re:Big O Notation – Explained as easily as possible
by thaumasiotes on Sunday January 17, 2021 @12:34AM
(#25808450)
> What irks me is people who use the equal sign as in T(n)=O(n log n), though. Why would a function equal a class? Set membership notation does the job just fine.
It's strange but it's fully standard. I would guess it develops from the use in analysis, where o(n) is more common. You derive your formula, it has a term in it that you don't want, you observe that "complicated term's numerator = o(n)", you take your limit, and the term vanishes away. Use of the = sign makes more sense there, because conceptually you're claiming something about the value of the term. (Specifically, that in the limit, it's equal to zero.)
It's strange but it's fully standard. I would guess it develops from the use in analysis, where o(n) is more common. You derive your formula, it has a term in it that you don't want, you observe that "complicated term's numerator = o(n)", you take your limit, and the term vanishes away. Use of the = sign makes more sense there, because conceptually you're claiming something about the value of the term. (Specifically, that in the limit, it's equal to zero.)