Re: infinity

From: David Kastrup <dak@xxxxxxx>
Date: Wed, 05 Oct 2005 23:52:39 +0200

"Jonathan Hoyle" <jonhoyle@xxxxxxx> writes:

> It certainly does not imply that. Well-ordering the reals will use a
> different <= operation than the normal ordering. What is required by a
> well-ordering is any comparison operation (which we denote <= but is
> not the usual less than or equal to) such that for any a,b in R either
> a<=b or b<=a

Strike the "either".

> and that any non-empty subset of R has a "first" element (in the
> sense of our new <=).

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

References:
- Re: infinity
  - From: Jonathan Hoyle
- Re: infinity
  - From: Ross A. Finlayson
- Re: infinity
  - From: Jonathan Hoyle
- Re: infinity
  - From: Jonathan Hoyle
- Re: infinity
  - From: Ross A. Finlayson
- Re: infinity
  - From: Jonathan Hoyle
- Re: infinity
  - From: Ross A. Finlayson
- Re: infinity
  - From: Jonathan Hoyle
- Re: infinity
  - From: Ross A. Finlayson
- Re: infinity
  - From: Jonathan Hoyle

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Relevant Pages

Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
... that every set has a well-ordering. ... So, it is known the set of reals, where the collection of all real ... some sequence of reals with the normal ordering. ...
(sci.math)
Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
... that every set has a well-ordering. ... So, it is known the set of reals, where the collection of all real ... some sequence of reals with the normal ordering. ...
(sci.logic)
Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
... there is at least one well-ordering of the reals. ... A well-ordering is necessarily a total ordering so the well-ordering ... always a greatest element in the normal ordering, ...
(sci.math)
Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
... there is at least one well-ordering of the reals. ... A well-ordering is necessarily a total ordering so the well-ordering ... always a greatest element in the normal ordering, ...
(sci.logic)
Re: On Well-Ordering(s) and Sets Dense in the Reals, Infinity
... Adding elements like iota doesn't help, ... > Well-ordering is a much more restrictive property than you think. ... _then_ the normal ordering of the non-negative ... reals would be a well-ordering of any non-empty subset of the ...
(sci.logic)