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**General Discussion / Re: Maths thread.**

« **on:**February 22, 2021, 05:43:40 pm »

f ∈ O(n^2)

If you write this, it's a shorthand for f ∈ O(g) where g : n ↦ n^2. But f(x) ∈ O(g(x)) is nonsensical because f(x) isn't a thing. f is a function; f(5) is a number, "f(x) = 3x" is a shorthand for f = {... (-1, -3), (0,0), (1,3), ...}. But f(x) itself is literally not anything.

What makes it acceptable to use n^2 as a shorthand for n -> n^2, but not f(x) as a shorthand for x -> f(x)?