[FOM] 622: Adventures in Formalization 6

[joeshipman at aol.com]

Yes, I was going to say that. And the rationals are also a subset of the reals in this system which contain the natural numbers as a subset.


You still need to adjoin an imaginary unit in the usual way to get the complex numbers though, there doesn't seem to be a simpler or more unified way to do it (according to Conway, who has looked for one for a long time).


-- JS



-----Original Message-----
From: Mitchell Spector <spector at alum.mit.edu>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Tue, Oct 27, 2015 7:16 pm
Subject: Re: [FOM] 622: Adventures in Formalization 6


With regard to the discussion as to whether the set of natural numbers should be
a subset of the set 
of real numbers, or whether it's good enough to have an
isomorphism that lets us identify natural 
numbers with certain real
numbers:

It may worth pointing out that Conway's surreal numbers provide a
systematic approach which includes 
both the natural numbers and the real
numbers, and which makes N a subset of R.

Mitchell Spector
Email:
spector at alum.mit.edu
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