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Re: Representing a set of value pairs?

From: Stan Devitt <jsdevitt@stratumtek.com>
Date: Sun, 20 Jul 2003 08:28:31 -0400
Message-ID: <3F1A8AEF.20006@stratumtek.com>
To: "Roger L. Costello" <costello@mitre.org>
CC: www-math@w3.org

As another example,  the set of squares of the  positive integers 
shifted by a constant c could be written

set (  bvar(i)  , condition ( i > 0 , member(i, integers) ) ,  i^2  + c )

which in a more conventional notation might be written

{  i^ 2+c  |   i > 0  and i in set of Integers } 

The use of bvars just makes  it explicit which of the terms in i^2 + c are
placeholders and which are constants which are part of the expression.

Stan Devitt
StratumTek


Roger L. Costello wrote:

>Thanks Stan.  Let me see if I understand you correctly.  Are you saying
>that when defining this set in MathML:
>
>    {i, c | c = i * 2.54}
>
>After specifying the set contents I need to specify the "set variables"
>(in this case they are "i" and "c")?  e.g., 
>
><set>
>  <bvar>...</bvar>
>  <condition>
>     ...
>  </condition>
>  <list><ci>i</ci><ci>c</ci></list>  <-- specify set variables here
></set>
>
>Is the purpose of:
>
>   <list><ci>i</ci><ci>c</ci></list>
>
>to indicate "these are the set variables"? 
>
>Is there an advantage of using <list>...</list> rather than set, i.e.,
>
>   <set><ci>i</ci><ci>c</ci></set>
>
>Thanks!  /Roger
>
>
>Stan Devitt wrote:
>  
>
>>This type of set constructor should have a final argument which is
>>a sample of the thing being constructed as in
>>
>><set>
>>  <bvar><ci>i</ci></bvar>
>>  <bvar><ci>c</ci></bvar>
>>  <condition>
>>  <apply><eq/>
>>    <ci>c</ci>
>>    <apply><times/>
>>      <ci>i</ci>
>>      <cn>2.54</cn>
>>    </apply>
>>  </apply>
>>  </condition>
>>  <list><ci>i</ci><ci>c</ci></list>
>></set>
>>
>>They should be grouped in some way, for example, using a set,
>>list or vector.
>>
>>Stan Devitt
>>StratumTek
>>
>>Roger L. Costello wrote:
>>
>>    
>>
>>>Hi Folks,
>>>
>>>Suppose that I want to represent the set of all inch/centimeter pairs,
>>>e.g,
>>>
>>>  {i, c | c = i * 2.54}
>>>
>>>Examples in this set include:
>>>
>>>  (1.0, 2.54), (2.0, 5.08), etc
>>>
>>>Is this the correct way to represent this set in MathML:
>>>
>>><math>
>>>   <declare type="set">
>>>       <ci>S<ci>
>>>       <set>
>>>           <bvar><ci>i</ci></bvar>
>>>           <bvar><ci>c</ci></bvar>
>>>           <condition>
>>>               <apply>
>>>                   <eq/>
>>>                   <ci>c</ci>
>>>                   <apply>
>>>                       <times/>
>>>                       <ci>i</ci>
>>>                       <cn>2.54</cn>
>>>                   </apply>
>>>               </apply>
>>>           </condition>
>>>       </set>
>>>   </declare>
>>></math>
>>>
>>>I think that this is correct.  My only hesitation is that perhaps I need
>>>parentheses around (i,c)?  e.g.,
>>>
>>>     {(i, c) | c = i * 2.54}
>>>
>>>And likewise in the MathML representation place parentheses?  /Roger
>>>
>>>
>>>
>>>      
>>>
>
>  
>
Received on Sunday, 20 July 2003 08:26:25 GMT

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