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