Sigh, even here, on an article whose very purpose is to point out that = does not mean equality as used by mathematicians, there are people calling this an abuse of notation. It's not; it's the standard notation in asymptotics. Using set-theoretic notation is cumbersome — you have to use “∈” in things like 3n^2 + 5 = O(n^2), but “⊆” in things like (n+O(√n))^2 = n^2 + O(n√n) — and defeats much of the point of using O() notation in the first place. I've mostly seen programmers / CS people insist on calling it abuse of notation and try to pedantically and counterproductively use set-theoretic notation, when mathematicians have been freely using the = sign for more than a century, from before the birth of computers. (Not repeating my comment from earlier: https://news.ycombinator.com/item?id=16834297)
Wow, so disagreeing with the point of this article immediately provokes a typed-out condescending sigh from you? That's worth a sigh more than anything. Furthermore, I was a mathematics person first, and got into computer science later, so I'm not a "CS person" insisting on calling it an abuse of notation.
I have two points:
Firstly, although the article does a good job making the point that there's no reason to get on programming languages' case for using formalized, ad hoc syntax, it does a terrible job of backing up it's actual title. The bottom line is the equals sign is very closely associated with the concept of RST equivalence in mathematics, to the point where a specificity such as the symbol for the isomorphism (which, ironically, he used as a counterexample) is abstracted away, because isomorphism is an RST relation. If two things are isomorphic, they are, in some sense, the same (or equal), so use of an equals sign is natural.
Secondly, if you had read the first source you posted, maybe you wouldn't have claimed programmers/CS people were the ones pedantically insisting on calling it an abuse of notation since, on page 6, Bruijin writes, "The trouble is, of course, due to abusing the equality sign =."[1] Furthermore, after defining the parameters around the use of the O-symbol, he also writes, on page 7, "It is obvious that the sign = is really the wrong sign for such relations, because it suggests symmetry, and there is no such symmetry."[1]
