I’ve never liked to conflation with fractions. Abuse of notation. And it causes so much confusion.
Also integrals with “integrate f(x) dx” where people treat “dx” as some number than can be manipulated, when it’s more just part of the notation “integrate_over_x f(x)”
Sigh. These are sadly some kind of right-of-passage, or mathematical hazing. Sad.
Ordinary derivatives work fine as fractions. They are rigorously the limit of a fraction. Same deal with dx inside the integral, it is rigorously the limit of a small \Delta x in a summation.
Baez is mixing partial derivatives with different variables treated as constants. Whole different ball game.
I consider it not an abuse of notation but a helpful notation. It insinuates correctly >90% of calculus rules, which tend to be hard to remember otherwise.
Comments
I’ve never liked to conflation with fractions. Abuse of notation. And it causes so much confusion.
Also integrals with “integrate f(x) dx” where people treat “dx” as some number than can be manipulated, when it’s more just part of the notation “integrate_over_x f(x)”
Sigh. These are sadly some kind of right-of-passage, or mathematical hazing. Sad.
Ordinary derivatives work fine as fractions. They are rigorously the limit of a fraction. Same deal with dx inside the integral, it is rigorously the limit of a small \Delta x in a summation.
Baez is mixing partial derivatives with different variables treated as constants. Whole different ball game.
I consider it not an abuse of notation but a helpful notation. It insinuates correctly >90% of calculus rules, which tend to be hard to remember otherwise.