3 ms·
Well, if you wanted to be precise you should specify for which indices x_i=y_i should hold. But if it's clear from the context then that might be left out. You
by contravariant 11y ago
Well, if you wanted to be precise you should specify for which indices x_i=y_i should hold. But if it's clear from the context then that might be left out.
You're definitely right that mathematics doesn't really have things like variables though. You're only allowed to define a symbol once, but then it doesn't necessarily need to have a specific value (e.g. you're allowed to define 'x' and 'y' implicitly using the equation 'x = 2yx', or less trivially 'x^2 + y^2 = 1').
- fallingfrog 11y agoYeah, the key insight I think is that if you don't put any constraints on some variable then the intent is that the equation is true for any choice of that variable- so since x_i = y_i for any i, then it's logically the same as saying x0 = y0, x1 = y1, ... It was an aha moment when I realized what they were doing there. Very elegant actually.