#8519: Add a factory of finite/infinite enumerated set (with categories) defines
by Range(begin, end, step)
-----------------------------+----------------------------------------------
   Reporter:  nborie         |       Owner:  nborie                         
       Type:  enhancement    |      Status:  new                            
   Priority:  major          |   Milestone:  sage-4.3.4                     
  Component:  combinatorics  |    Keywords:  range, categories, set, integer
     Author:                 |    Upstream:  N/A                            
   Reviewer:                 |      Merged:                                 
Work_issues:                 |  
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Changes (by nborie):

  * keywords:  positive integer => range, categories, set, integer


Old description:

> We have already a proper set with category of NonNegativeIntegers, let's
> use it to also define PositiveInteger
>
> {{{
> sage: NonNegativeIntegers()
> Non negative integers
> sage: PositiveInteger()
> ---------------------------------------------------------------------------
> NameError                                 Traceback (most recent call
> last)
>
> /home/nicolas/<ipython console> in <module>()
>
> NameError: name 'PositiveInteger' is not defined
> }}}

New description:

 A general tool to define:
 - PositiveInteger
 - NonNegativeInteger
 - More.....

 The idea is :
 Range(begin, end, step) returns a proper finite/infinite set with
 categories of the defined set as you think...

 (12:37:41) hivert: For example but not only: Range(5, 2^1321312, 3)...
 (12:38:09) hivert: Range(0, Infinity, 1) <=> NonNegativeIntegers
 (12:38:18) hivert: Range(1, Infinity, 1) <=> PositiveIntegers

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8519#comment:2>
Sage <http://www.sagemath.org>
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