2 ms·

I'd say that the = is one of the most annoying abuses of notation that I know of, if not the most. Apart from not symmetric, which is a problem in its own right

I'd say that the = is one of the most annoying abuses of notation that I know of, if not the most. Apart from not symmetric, which is a problem in its own right, for small o and small omega it's not even reflexive, which does not prevent the = users from using it also for those. Which amounts to using an equals sign to highlight how two functions differ. And what do people gain with that? It's not as if a set membership symbol, which works just fine because big O, small o, the omegas and their ilk define sets of functions, doesn't work just fine and take the same space without being confusing.

edflsafoiewq 6y ago
The notation is from math; the point of it is that you can manipulate it like a normal expression, but it's "anonymous"; o(1) means some function that goes to zero, but we don't bother with a name, just recording the asymptotic behavior. For example, f'(x) = lim (f(x+h)-f(x))/h can be rewritten with an error term f'(x) = (f(x+h)-f(x))/h + o(1), and then you can manipulate it more freely, say like f(x+h) = f(x) + hf'(x) + o(h). There's no need to drag out a bunch of useless names, each qualified by a set membership, to do this. I mean e(h) in o(1), e2(h) := h e(h) in o(h), etc. The failure of "reflexivity", eg O(f) = O(f), is because the anonymity hides whether the two O(f)s are referring to the same function (ie. exactly what a name would tell us).