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/
>
>
>
>
> >
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