Re: Defining "<" for the rationals

In article <43888E55.5060006@xxxxxx>, Jannick Asmus writes:
>On 26.11.2005 17:21, Michael Stemper wrote:
>> I've been looking at the rational numbers as an equivalence relation.

>> I wanted to also define the "<" relation, but hit a stumbling
>> block.

>> seem particularly elegant. Is there a cleaner way to define the less
>> than relation on rationals?

>If you require the relation < to be compatible with addition in the
>obvious way, you could reduce the situation by defining when a rational
>is positive.

I was hoping to use this result to define a positive rational number
as one that satisfied (0,1)<(a,b). Shoot!

--
Michael F. Stemper
#include <Standard_Disclaimer>
Always use apostrophe's and "quotation marks" properly.

.

Relevant Pages

  • Defining "<" for the rationals
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  • Re: Defining "<" for the rationals
    ... >On 26.11.2005 17:21, Michael Stemper wrote: ... >> I've been looking at the rational numbers as an equivalence relation. ... Is there a cleaner way to define the less ... >> than relation on rationals? ...
    (sci.math)
  • Re: Defining "<" for the rationals
    ... On 26.11.2005 17:21, Michael Stemper wrote: ... > I've been looking at the rational numbers as an equivalence relation. ... Is there a cleaner way to define the less ... > than relation on rationals? ...
    (sci.math)
  • Re: Defining "<" for the rationals
    ... > than relation on rationals? ... and denominator share no positive integer factor larger than 1 AND that ... the denominator be positive. ... you can define your equivalence relation on the Cartesian ...
    (sci.math)
  • Re: Defining "<" for the rationals
    ... >>> I've been looking at the rational numbers as an equivalence relation. ... >>> than relation on rationals? ... you can define < by requiring ...
    (sci.math)