@axiom @11011110 Exactly. I used "<" in the sense of "strict subset" (maybe I should have used "⊂").

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.

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?

axiom@axiom@mathstodon.xyz@11011110 @0foldcv strict subset