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  

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}.




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