> The equal sign does mean equals. In the particular case of big-O notation, the equals sign does not mean equals. Trying to parse the equal sign literally lea

> The equal sign does mean equals. In the particular case of big-O notation, the equals sign does not mean equals. Trying to parse the equal sign literally leads to confusing and contradictory interpretations (which is why their explanation is confusion). You're misunderstanding the 3=5 example. Let f(n)=3n, let g(n)=5n. Using big-O notation, f(n)=O(n), g(n)=O(n). Were the equal sign behaving normally, then O(n) would be a single well-defined object, and one could use transitivity to conclude that 3n=5n. But of course this is false, because O(n) isn't a single function, nor really something that other functions can equal. It's a class of functions, not a function itself. It would be more appropriate to say that "f(n) belongs to O(n)," or more compactly, "f(n) ∈ O(n)." This is much closer to the real definition, and behaves appropriately when taken literally.