As a layperson who is interested in math, imaginary numbers always fascinated me. Like in the real world you taking the square of a negative makes no sense whatso ever, but in theoretical math you can just invent new imaginary numbers, make it so that *i*^2 = -1 and suddenly you have just revolutionized math. If this is useful, why can’t you break other rules and account for them with new imaginary symbols?
So let’s pretend that we call them made up numbers and use *m* to represent them. Why is *m*=1/0 impossible when something like *i*^2 = -1 is not?
In: 27
The one easy way to illustrate why dividing by zero is problematic is to literally see what happens to 1/x as it approaches 0.
If you approch from the right (positive numbers), it races off to positive infinity. If approached from the left (negatives) it races off to negative infinity. In other words, it’s two literally opposite things at once. A contradiction. It just doesn’t behave nicely.
If I recall properly, there are attempts to define 1/0 as a new number similarly to i, but it keeps causing problems. I honestly don’t know the details, though.
In comparison, i has well defined properties and complex numbers not only don’t introduce contradictions, but solve a few other problems along the way.
Latest Answers