Path: dp-news.maxwell.syr.edu!spool.maxwell.syr.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newshub.sdsu.edu!newscon04.news.prodigy.net!prodigy.net!newsdst01.news.prodigy.net!prodigy.com!postmaster.news.prodigy.com!newssvr25.news.prodigy.net.POSTED!88885bfe!not-for-mail From: "Brian Selzer" Newsgroups: comp.databases.theory References: <1159625559.607066.76970@i42g2000cwa.googlegroups.com> <1159638303.513871.92440@m73g2000cwd.googlegroups.com> <1159692483.421785.264660@c28g2000cwb.googlegroups.com> <1159882356.495737.117850@i42g2000cwa.googlegroups.com> <96jdi251552m2rb54f8edjrmhitcld1kni@4ax.com> <8VWWg.1111$P92.756@trndny02> Subject: Re: Proposal: 6NF Lines: 74 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.3790.1830 X-RFC2646: Format=Flowed; Original X-MimeOLE: Produced By Microsoft MimeOLE V6.00.3790.1830 Message-ID: NNTP-Posting-Host: 68.73.73.118 X-Complaints-To: abuse@prodigy.net X-Trace: newssvr25.news.prodigy.net 1160532807 ST000 68.73.73.118 (Tue, 10 Oct 2006 22:13:27 EDT) NNTP-Posting-Date: Tue, 10 Oct 2006 22:13:27 EDT Organization: SBC http://yahoo.sbc.com X-UserInfo1: TSU[@I_A\S@WR_\YBRMNO_TDFZ\@@FXLM@TDOCQDJ@_@FNHBK^RAQFW[ML\THRCKV^GGZKJMGV^^_JSCFFUA_QXFGVSCYRPILH]TRVKC^LSN@DX_HCAFX__@J\DAJBVMY\ZWZCZLPA^MVH_P@\\EOMW\YSXHG__IJQY_@M[A[[AXQ_XDSTAR]\PG]NVAQUVM Date: Wed, 11 Oct 2006 02:13:27 GMT Xref: dp-news.maxwell.syr.edu comp.databases.theory:45684 "David Cressey" wrote in message news:8VWWg.1111$P92.756@trndny02... > > "Hugo Kornelis" wrote in message > news:96jdi251552m2rb54f8edjrmhitcld1kni@4ax.com... >> On Fri, 06 Oct 2006 12:59:15 GMT, David Cressey wrote: >> >> >There is one point I'm confused on: what is the domain of the empty >> >set? >> >does it even have a domain? To me, the empty set of character strings > is >> >not "the same thing" as the empty set of integers. But I may be >> >thinking >> >like a computer person and not like a mathematician. >> >> Hi David, >> >> Here are some thoughts from someone who is far from a mathematician and >> who is more a database practictioner than a database theorist, so take >> them with whatever amount of salt you see fit. >> >> When I worked with sets during the Dutch equivalent of highschool, I >> usually had to use a two-part notation. I can't replicate the symbols >> here and I don't recall all the correct names, but it consisted of a >> definition of a domain and a listing or formula to define the values. So >> you could have a set that was defined as a subset of the domain of >> positive integers consisting of the numbers 2, 4, and 7; but you could >> also have a set defined as a subset of the domain of real values >> consisting of the numbers 2, 4, and 7. >> Later, after highschool, I started to see a simplified notation for sets >> that exposes only the values in the set but not the domain. >> >> Are the two sets above equal? I guess that you could defend both answers >> here - the sets have the same members, but not the same domain >> definition. I also guess that the notation used can sometimes be an >> indication of how the answer would be in any give UoD. >> >> For a general answer, I'm tempted to say that there have to be two >> equality operators for set arithmetic, one looking at the values of the >> set members only, the other also looking at the domain. >> >> Anyway, whatever you favor as an answer to the question of equality of >> the two sets above - once you've chosen an answer, the answer to >> equality of two empty sets logicallly follows. >> >> Best, Hugo > > Thanks for your reply, Hugo. I'm also more of a practitioner than a > theoretician, and certainly no mathematician. > So I'll take what you say with a grain of salt, and you can do the same > with > what I say. > > It's not clear to me that the real number 2 is the same thing as the > integer > 2. Just for clarity, let me represent the real number 2 as 2.0. It > seems > to me that {2.0, 4.0, 7.0} is not equal to {2, 4, 7} the elements are > counterparts, but they aren't the same. > Hi David The domain of integers is a proper subset of the domain of reals. I think the concept is called "specialization by constraint." That means that every integer is also a real number; therefore, {2, 4, 7} is identical to {2.0, 4.0, 7.0}. 2.0 and 2 are just possible representations of the same number, which belongs not only to the set of all real numbers but also to the set of all integers. --Brian