As a layperson who is interested in math, imaginary numbers always fascinated me. Like in the real world you taking the square of a negative makes no sense whatso ever, but in theoretical math you can just invent new imaginary numbers, make it so that *i*^2 = -1 and suddenly you have just revolutionized math. If this is useful, why can’t you break other rules and account for them with new imaginary symbols?
So let’s pretend that we call them made up numbers and use *m* to represent them. Why is *m*=1/0 impossible when something like *i*^2 = -1 is not?
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You could write a consistent set of rules where you’re allowed to “divide by zero,” whatever that means to you, and it’d still be math. I’ve taken a math class where we redefined addition and multiplication to mean something different and then investigated whether specific sets were vector spaces under those definitions. All math is made up by people.
It would then be up to you to persuade other people that your set of mathematical rules was interesting and worth studying. Many mathematicians have been persuaded that i^(2)=-1 makes for an interesting set of rules, both because it’s useful for electrical engineering and because it helps them achieve insights on problems they care about. None of the most popular systems of mathematical rules allows dividing by zero, but if you develop a good one and can argue for it persuasively, maybe you can change that.
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