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?
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The problem with dividing by zero, or, more properly having a zero in the denominator is that it could literally be anything. We call it undefined, but I think it is better described as ambiguous. Say you have 2/0, I have handed you two things but you have no idea whether they are half of something or 533rds of something. The number i is a placeholder but it is always only one thing. That is to say, it is unexplainable but definable and predictable, something a ratio with a zero denominator can never be.
Compare it to having a 0 in the numerator, you know the line or quantity was evenly divided once thereby creating 2 equal sets or lines. If I hand you none of those equal sets, your ratio is defined as zero. If I hand you two of the resulting sets for 2/2, you have all of the even subsets and therefore your ratio is just the whole number of 1. You can do this up to infinitesimally close to infinity in the nuker provided your denominator is >0.
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