@0foldcv I don't remember ever seeing this combination of < and O. Is it supposed to mean something different than = O(...)?
Saying something like
O(log(n)) = O(n) seems too much of an abuse of notation for my taste (because O(n) = O(log(n)) is false).
Not sure if "=" is always an abuse of notation for Landau symbols, but at least it's convenient for things like f(x) = g(x) + O(x²). In the previous case, I would prefer it meant equivalence.
@11011110 @axiom I agree with you for statements involving a function on the left hand side, such as f(x) = O(g(x)), as I mentioned before.
But do you not think that it’s confusing to write “O(log(n)) = O(n)”, when what meant is “f(n) = O(log(n)) implies that f(n) = O(n)”?
What notation would you have used for the chain of strict subset relationships in my original post?
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