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 -~----------~----~----~----~------~----~------~--~---