I believe this is slighly incorrect. In the very first chapter of many algebra/trig/calculus textbooks there's something to the effect that we study y = f(x), where there is only one solution for f(x). In other words, linear. As a kid I wondered why 1/0 was undefined. I only learned at the end of linear algebra, in college, when it came to inverse functions.
We know that x * 0 = 0, for any value of x. However, if we take the inverse operation of multiplication (that is, division), there is an infinite number of solutions for x / 0. Since we're operating in a linear system where there's only one solution for y = f(x), having more than one solution is undefined.
Clear as mud... This is why Feynman was a genius and I am not.