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
Let me show you a cool algebra trick
Let’s start with:. a = b
Now let’s add a to both sides
2a = a + b
Now subtract 2b from both sides
2a – 2b = a – b
Factor the left side
2(a – b) = a – b
Now finally divide by (a-b)
2 = 1
Seems like a strange result! I was able to get this result because I was sneaky and I divided by 0 in the last step. If a = b, then (a-b) is 0. When you divide by 0, strange things happen. Once you prove 2 = 1, you can really just prove that anything = anything else. To avoid that, we say you can’t divide by 0.
But what’s stopping us from dividing by 0 and making up our own rules about how it works? Well nothing really. You can make up your own math if you’d like. But your biggest challenge for that made up math is going to be how you make sure that 2 and 1 are separate numbers. Cuz I say they’re equal if you can divide by 0.
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