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
If you and I share a pie, how do we divide it? 1 / 2 = 1/2, or .5
If you have a pie to yourself, how should you divide it? 1/1=1, you don’t have to divide it
If nobody has a pie, how should it be divided? Or 1/0=… Divide amongst whom? Why? You can see it’s a nonsense question. It can’t be answered in a meaningful way for most purposes
Imaginary numbers answer meaningful questions with useful results in predictable ways. When you pose division by zero as a word problem it becomes evident that you’re not really asking anything applicable to normal situations. Eg: it’s nonsense. Which we more charitably call undefined
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