Every story and comment from the Hacker News API, in a layout borrowed from 2001.
A comment on Notation as a Tool of Thought (1979). Parent comment
1) The differential of a function (at a point), dy, is not notation, it is a concept.
2) The differential of the function y = x, dx, is not, then, a notation, either; and, since the derivative is 1, dx = 1 Δx = Δx = x - x0.
3) You can argue, of course, that using dx instead of Δx in dy = f'(x)dx is "notation," but I think the above shows that it is more than that.
There are no comments on this comment yet.
1) The differential of a function (at a point), dy, is not notation, it is a concept.
2) The differential of the function y = x, dx, is not, then, a notation, either; and, since the derivative is 1, dx = 1 Δx = Δx = x - x0.
3) You can argue, of course, that using dx instead of Δx in dy = f'(x)dx is "notation," but I think the above shows that it is more than that.