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

810 views

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

19 Answers

Anonymous 0 Comments

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

You are viewing 1 out of 19 answers, click here to view all answers.