Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?

Question

Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?

In: Mathematics

Answer 1

You can, and people have.

Creating an imaginary number that breaks the rules of squaring a negative produces a useful concept that can be used to explore things like imaginary roots of polynomials, which helps with things like typing solutions to differential equations. So far, there has been absolutely no useful application of a concept that allows you to divide by zero, and it also comes with the added complication of creating many more problematic hiccups in your math, such as allowing 1=2.

I challenge you to define a new symbol, &, where &/0=1, and produce a useful result with it.