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My understanding is that numbers are grouped in a sort of Russian doll fashion, with each successive group encompassing all previous ones. I suppose there is an infinite number of ways to define these groups, but the way I order them goes like this:

-Natural numbers

-Rational numbers

-Real numbers

-Complex numbers

Now, since complex number require the special definition of √(-1), could you just define division by zero (arbitrarily, say, as "1/0 = m") and make an even more general number group?