The fish eating cat math meme is soo humorous and wholesome. I laughed out of breathe , the first time I saw that one.,(reply>), @Tonio Kettner I see what you're saying. I'm just used to seeing the identity as some version of 1. Like how the nxn identity matrix is the nxn square matrix with ones on its main diagonal and zeros elsewhere.<br><br>As for the fish thing, I was imagining the function as a cat eating a fish and the inverse as a fish eating a cat. So if we apply the function and have a cat eat a fish, only the cat would be here still. But if we apply the inverse and have a fish eating the cat we got from applying the function, we would once again be left with a fish. So by that logic f^-1(f(fish))=fish. Sure it obviously wouldn't be the same fish we began with, but this is pure math. We don't need to worry about the real world here haha.,(reply>), @Xavier Stanton first of all: x is the identity of all functions f: ℝ → ℝ when you use x as your input variable.<br>second:<br>a fish eating a cat eating a fish ≠ a fish,(reply>), @Tonio Kettner I hate to sound mean, but that is not the definition. The inverse function is defined such that F^-1(F(x))=x, not the identity. <br><br>So if x=fish, the joke works out fine,(reply>), @Xavier Stanton you don't understand: the inverse function f^-1 is defined such that (f^-1 o f) = id, which is not true at all with the fish and cat,(reply>), @Tonio Kettner That isn't the joke. The joke is that if the function is cat eating fish, the inverse function would be the fish eating the cat.