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We first define the natural numbers, then negative numbers, then fractions(rationals), then the real numbers, and then complex numbers. The reason we start with naturals is probably that we used our fingers as counting objects and hence natural numbers are essentially... natural. This is a related post- Numbers, is there any scope beyond? but it is a little different from what I'm asking.

I was wondering if there was another system where after defining numbers (or whatever they might be), we would end up with another form of consistent mathematics? Or is it that this system is unique? Can we prove it?

Thanks in advance

thedumbkid
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  • Do you mean something like this? https://en.m.wikipedia.org/wiki/P-adic_number – Maximilian Janisch Aug 29 '20 at 00:15
  • Not sure what you mean. There are other types of numbers, not only complex. The $p$-adic numbers (which were mentioned in the previous comment) are one example. – Mark Aug 29 '20 at 00:16
  • Thanks a lot for that. I did not have the knowledge about p-adic numbers. Yes I did mean something like that. – thedumbkid Aug 29 '20 at 09:39

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