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
Defined by what, though? Take any random fraction, let’s say, 6/2=?. Let’s replace the question mark and do some simple algebra. Now you have 6=x*2. Now you should clearly see a/b=c is the same as a=c*b. Now there’s a problem when b=0 *because* no matter what number you multiply with the result is always 0 and cannot be a. Let’s see that in action using 6/0
6/0=x
6=0x
These 2 equations are equivalent due to the formal rules of algebra. But let’s throw out the rules and try it anyway. So let’s define the answer to zero division as @ and try those 2 equations again
6/0=@ Seems legit, let’s continue
6=0*@
Uh oh. Now there’s a problem because no matter what @ “equals”, when multiplied by 0 the result is always 0. And 6=0 is false
Let’s even look at this another way. As children we were taught basic division by repeated subtraction. So 6/2, if you have 6…idk…apples. Yes 6 apples, and you remove 2, you now have 4 apples. Remove 2 again and you have 2 apples. Remove the last 2 and you have no more apples. So 6/2 equals 3. But what happens when you remove *no* apples? There is no change. In other words 6-0=6. No matter how many times you repeat this it will **always** be 6. Sometimes people try to say the result of zero division is infinity, but you should see very clearly that isn’t true either. And even if it was true, infinity is also undefined lol
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