[FOM] 622: Adventures in Formalization 6

joeshipman at aol.com joeshipman at aol.com
Tue Oct 27 20:12:10 EDT 2015

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

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
spector at alum.mit.edu
mailing list
FOM at cs.nyu.edu

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