Why is it mathematically consistent to allow imaginary numbers but prohibit division by zero?

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Couldn’t the result of division by zero be “defined”, just like the square root of -1?

Edit: Wow, thanks for all the great answers! This thread was really interesting and I learned a lot from you all. While there were many excellent answers, the ones that mentioned Riemann Sphere were exactly what I was looking for:

https://en.wikipedia.org/wiki/Riemann\_sphere

TIL: There are many excellent mathematicians on Reddit!

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Anonymous 0 Comments

It’s not necessarily that it’s prohibited. You *could* define an imaginary number to the result of dividing by zero. It’s just that it’s not useful so what is the point?

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