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
Full disclaimer: I don’t think there’s a way to ELY5 on this one.
So, imaginary numbers have been given a bad rap; they’re not made up or invented or anything, they exist. They’re a different “dimension” of value. It’s not gonna really make sense in a day-to-day type of explanation because they don’t describe a value we interact with in our everyday lives, the same way numbers in the real number kingdom do. But they do describe a value, a particular piece of information. That’s what numbers do; they’re descriptors of value. Think about two: two is two ones, it’s four halves, it’s three less than five, it’s eight more than negative six, it’s the square root of four. These are all functions that describe the value of two and no other value. The problem with attempting to “divide by zero” is that the function doesn’t define any particular value. It’s actually called “undefined” for that very reason. If you were to attempt to use mathematics to approximate an answer to 1/0, you might find that your ‘answer’ could equal +/- infinity (which doesn’t really work in mathematics, infinity is a concept, not a value). And then you find that you get the same ‘answer’ when you try 2/0, or 3/0, or any other value.
Basically, dividing by zero doesn’t describe a value; it’s just kinda mathematical nonsense, but the square root of negative one _is_ an actual value, just not one that exists in the same dimension as values we’re traditionally familiar with.
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