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 problem with “defining” the result of dividing by 0 is that it could be anything, depending on the context, so the result would be fairly meaningless without that context.
The way we can reason about this comes from calculus, specifically limits if you want to look it up more – consider a function such as 1/x. When x gets really small, 1/x gets really big. For example, 1/0.0001 = 10000. But, if x is negative, x gets really big and negative. This means that from one side, it’s negative infinity, and from another side, it’s positive infinity. These are two different values.
Consider a different function, x/x. Anywhere except where x = 0, this function is 1. In fact, we can also say the limit at x = 0 is 1. But we still can’t say that 0/0 actually is 1 because in other contexts it’s something else.
Outside of the context, the value is useless – within the context, we have the concept of limits to formally reason about divisions by 0.
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