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!
In: 1691
Mathematics doesn’t really have any global rules. Operations are defined in some contexts and not in others, depending on what is interesting or useful. For example, if you’re modelling a population of animals, you might well forbid negative or fractional numbers of animals, let alone complex numbers.
There are systems in which division by zero is defined, like the extended real numbers, but they aren’t really all that interesting, and it’s almost always more convenient to leave it undefined. The complex numbers have a very interesting structure that is convenient to use in many contexts.
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