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From: "Prof. Peter Johnstone"
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Subject: Re: "Kantor dust"
Date: Sun, 8 Feb 2009 14:51:19 +0000 (GMT)
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To: Toby Bartels ,
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On Sat, 7 Feb 2009, Toby Bartels wrote:
>> Toby was of course referring to the Dedekind reals
>
> Actually, I was trying to keep it open,
> since different schools of constructivism have different opinions
> about which are the correct reals (as well as which are equivalent).
> But nobody uses the binary reals, since they can't subtract them.
Never mind subtraction -- you can't even add them. As I mentioned in my
last posting, the question "Is x < 1/2?" is decidable for Vaughan's binary
reals, but "Is x < 1/3?" is not (constructively), so the operation
of adding 1/6 can't be defined.
Peter Johnstone