Bruno, Yes, this seems very clear and will be helpful to refer back to if necessary. m.a.
----- Original Message ----- From: "Bruno Marchal" <marc...@ulb.ac.be> To: <everything-list@googlegroups.com> Sent: Sunday, June 07, 2009 4:33 AM Subject: Re: The seven step-Mathematical preliminaries 2 > > Marty, > > On 07 Jun 2009, at 02:03, Brent Meeker wrote: > >> >> m.a. wrote: >>> *Okay, so is it true to say that things written in EXTENSION are >>> never >>> in formula style but are translated into formulas when we put them >>> into INTENSION form? You can see that my difficulty with math >>> arises from an inability to master even the simplest definitions. >>> marty a.* >> >> It's not that technical. I could define the set of books on my >> shelf by >> giving a list of titles: "The Comprehensible Cosmos", "Set Theory and >> It's Philosophy", "Overshoot", "Quintessence". That would be a >> definition by extension. Or I could point to them in succession and >> say, "That and that and that and that." which would be a definition by >> ostension. Or I could just say, "The books on my shelf." which is a >> definition by intension. An intensional definition is a descriptive >> phrase with an implicit variable, which in logic you might write as: >> The >> set of things x such that x is a book and x is on my shelf. > > > This is a good point. A set is just a collection of objects seen as a > whole. > > A definition in extension of a set is just a listing, finite or > infinite, of its elements. > Like in A = {1, 3, 5}, or B = {2, 4, 6, 8, 10, ...}. > > A definition in intension of a set consists in giving the typical > defining property of the elements of the set. > Like in C= "the set of odd numbers which are smaller than 6". Or D = > the set of even numbers. > > In this case you see that A is the same set as C? And B is the same > set as D. > > Now in mathematics we often use abbreviation. So, for example, instead > of saying: the set of even numbers, we will write > {x such-that x is even}. > > OK? > > Bruno > > > > > Suppose, > > > > > > http://iridia.ulb.ac.be/~marchal/ > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---