Re: finite domains

*To*: mathgroup at smc.vnet.net*Subject*: [mg53053] Re: finite domains*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 22 Dec 2004 04:52:43 -0500 (EST)*Organization*: The University of Western Australia*References*: <cp3t2v$9ai$1@smc.vnet.net> <200412201134.GAA02658@smc.vnet.net> <cq8u48$h47$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <cq8u48$h47$1 at smc.vnet.net>, János <janos.lobb at yale.edu> wrote: > I looked at the article and I understand that for that particular case. > However that case fell back in the definition on an already existing > infinite domain of the same order namely Z. There is also a similar > definition in the Book for Odd numbers. > > In my case I cannot fall back on an existing finite domain, or I do not > know how to explore/exploite it with Boolean. > > I am thinking of a domain named Irany having elements > {North,East,South,West}. How can I do that without a reference to a > more basic domain as foundation and expect that > Element[NorthWest,Irany] will give me False? The following code does what _you_ want: Irany /: Element[x_, Irany]:= MemberQ[{North,East,South,West}, #]& /@ x Element[{North, West}, Irany] Element[NorthWest, Irany] However, this violates the "spirit" of Mathematica because, for an arbitrary symbol, the definition should return the unevaluated expression -- but if you try Element[y, Irany] you get false, rather than the unevaluated expression. Now, y could be North, or it could be NorthWest ... Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul

**Follow-Ups**:**Re: Re: finite domains***From:*János <janos.lobb@yale.edu>

**References**:**Re: finite domains***From:*Paul Abbott <paul@physics.uwa.edu.au>