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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There’s a lot of helpful stuff here about why 1/0 causes problems in “regular” math — but you’re exactly right that we can define it anyway! That’s what happened with negative numbers (from positives), rational numbers (from integers), irrational numbers (from rationals), and complex numbers (from reals) — none of them fit with all the axioms of previous, simpler systems of numbers, but mathematicians found them all useful enough that they (eventually) figured out new axioms that could correctly describe the behavior of these new numbers. Take a look here to see how adding 1/0 to the club changes things: [https://en.wikipedia.org/wiki/Projectively_extended_real_line#Dividing_by_zero](https://en.wikipedia.org/wiki/Projectively_extended_real_line#Dividing_by_zero)
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