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We can define integers in a similar manner starting from natural numbers: https://en.wikipedia.org/wiki/Integer#Construction

And rational from integers.

We agree that integers are generalization of natural numbers, as complex are generalization of reals.

So, shouldn't it be possible and easier to do the opposite? (Shouldn't it be easier to define a subset?)

I mean, it should be possible to define real numbers starting from complex numbers, but I can't think of any way. Sure, I can say (a,0) are real numbers, but in this way I already know and I'm already assuming that a,b∈ℝ in (a,b).

I hope my question is clear. Thanks.