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[OT] Re: linear programming

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Martijn van Buul wrote:

> * gwowen:
>> Usually yes.  But this is phrased like'If "something" satifies
>> "condition A", then we say it is "A-ified".'  In English-as-she-is-
>> used-by-mathematicians that's *a definition* of "A-ified".
> 
> Uh, most mathematicians I know would have used "if and only if" or
> any of its alternatives in that case; in writing it would've been 'iff'.

That does not match my experience. In _defintions_ you don't say "if and 
only if". Examples:

  A group G is called commutative or abelian if ab=ba for all a,b in G.

Or:

  A group G is called commutative or abelian if its group law is 
  commutative.

I am not aware of a mathematician who would use "if and only if" within a 
definition, e.g.:

  A group G is called abelian if and only if ab=ba for all a,b in G.

Of course, there is this mixture of theorem and definition, where you say 
something like: "For a ring R, the following three conditions are equivalent 
...; if any of them holds for R, we call R noetherian." Note, however, the 
"if" in the definition part of that statement. This is, what I think feels 
most natural to a mathematician.


To verify this point, you can check for instance in the following standard 
literature for the definition of a commutative group:

  Isaacs: Algebra, a graduate course (page 11)
  Bourbaki: Elements of Mathematic, Algebra 1 Chapters 1 - 3; 
            1.4.2 (page 31)
  Lang: Algebra (3rd ed), page 4 bottom
  Rotman: Advanced Modern Algebra; Groups I Chapter 2 page 52

In all cases, you will find "if" used instead of "if and only if". I cite 
those books not (just) as an apeal to authority. The graduate courses based 
upon those books shape the mathematical jargon of trained mathematicians. 
Hence, linguistic inclinations are picked up from those patterns.


Of course when it comes to theorems, mathematicians do distinguish very 
precisely a mere implication from an equivalence.



Best,

Kai-Uwe Bux

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linear programming eric <cneric12lin0@gmail.com> - 2011-06-19 20:53 -0700
  Re: linear programming "Alf P. Steinbach /Usenet" <alf.p.steinbach+usenet@gmail.com> - 2011-06-20 08:36 +0200
    Re: linear programming eric <cneric12lin0@gmail.com> - 2011-06-20 00:58 -0700
      Re: linear programming "Alf P. Steinbach /Usenet" <alf.p.steinbach+usenet@gmail.com> - 2011-06-20 11:38 +0200
    Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-20 03:07 -0700
      Re: linear programming "Alf P. Steinbach /Usenet" <alf.p.steinbach+usenet@gmail.com> - 2011-06-20 14:09 +0200
        Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-20 05:59 -0700
          Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-20 06:03 -0700
          Re: linear programming Martijn van Buul <pino@dohd.org> - 2011-06-20 15:13 +0000
            Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-20 08:38 -0700
              Re: linear programming Martijn van Buul <pino@dohd.org> - 2011-06-20 19:24 +0000
                Re: linear programming Gareth Owen <gwowen@gmail.com> - 2011-06-21 06:30 +0100
                Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-21 00:17 -0700
            [OT] Re: linear programming Kai-Uwe Bux <jkherciueh@gmx.net> - 2011-06-20 21:56 +0200
              Re: linear programming eric <cneric12lin0@gmail.com> - 2011-06-20 17:27 -0700
  Re: linear programming "Paul" <pchristor@yahoo.co.uk> - 2011-06-20 11:17 +0100
  Re: linear programming gwowen <gwowen@gmail.com> - 2011-06-20 03:07 -0700
  [OT] Re: linear programming Kai-Uwe Bux <jkherciueh@gmx.net> - 2011-06-20 19:38 +0200

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