Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?
In: Mathematics
As a math major, the closest I’ve come to dealing with division by zero is using limits. This means you divide by numbers approaching zero and see how the result responds. You must do this both from the negative (very small negative numbers) and positive very small positive numbers. There are basically 4 cases:
1. Both sides approach positive infinity. Therefore the limit of x/0 = infinity
2. Both sides approach negative infinity => negative infinity
3. Both sides approach 1 (since it’s essentially 0/0) => 1
4. The sides approach different values (infinity on one side, negative infinity on the other side, etc). In this case, it’s undefined
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