√ x when x < 0 was impossible using real numbers. Then, one day some guy decided that i = √ -1 and suddenly we can work with negative square roots. Which is still quite weird, but I suppose is valid (?)
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But there still stuff we can’t calculate in any of the number sets we have. Something we see much earlier than roots: division by 0.
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I get why x / 0 = x is false. Basically that would mean that 1 = 0, which is absurd (reductio ad absurdum). Ok. I don’t quite get why x/0 = 0 is false, but I’m sure there’s a contradiction somewhere that would make this impossible (if it was that simple, division by 0 would have been solved thousand of years prior). But if we can simply invent a number that doesn’t exists and it can fit maths no problem such as i = √-1 why can’t we make a number n = 0^(-1)?
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I also know the concept of limits but lim x->0 f(x) just means that x gets really close to the value of 0 but is never quite there so yeah, I don’t think that solves the issue.
In: Mathematics
The reason they made the square root of -1 the letter i is because complex numbers are very useful in many different applications. There is no real use for x/0, so we call it undefined, or not a number.
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