Re: The seven step-Mathematical preliminaries 2

```Bravo Thunderbird!
```
```
On 07 Jun 2009, at 18:39, m.a. wrote:

>
>> Bruno et. al.,
>>                        Good news! I have discovered that the math
>> symbols copy faithfully here in my Thunderbird email. Henceforth, I
>> will open all list letters here. Please refresh my memory for the
>> following symbols:

>>
>>
>> 1. The   ∅  is called___THE EMPTY SET_____and means______THE SET
>> WITH NO ELEMENTS

The empty set described in extension: { }
The empty set described in intension. Well, let me think. The set of
french which are bigger than 42 km tall.
A cynical definition would be: the set of honest politicians.
A mathematical one: the set of x such that x is different from x.
It is just the set which has no elements. It is empty.

>>
>> 2. The    ∪  is called________UNION______and means: A ∪ B__= {x
>> such-that x belongs to A  or x belongs to B};

>> A u B is the set obtained by doing the union of A and B.

>> 3. The   ∩   is called_____INTERSECTION____and means__A ∩ B__=
>> {x such-that x belongs to A  andr x belongs to B};     A u B is the
>> set obtained by doing the intersection of A and B. It is the set of
>> elements which are in both A and B._

Examples:

{1, 2, 3} ∩ {2, 4, 3} = {2, 3}
{1, 2, 3} u {2, 4, 3} = {1, 2, 3, 4}

{1, 2, 3} ∩ {4, 5, 6} =   ∅
{1, 2, 3} u {4, 5, 6} = {1, 2, 3, 4, 5, 6}

OK?

Bruno

>>
>>
>>  ----- Original Message -----
>>       From: Bruno Marchal
>>       Sent: Wednesday, June 03, 2009 1:15 PM
>>       Subject: Re: The seven step-Mathematical preliminaries 2
>>
>>
>>       ∅ ∪ A =
>>       ∅ ∪ B =
>>       A ∪ ∅ =
>>       B ∪ ∅ =
>>       N ∩ ∅ =
>>       B ∩ ∅ =
>>       ∅ ∩ B =
>>       ∅ ∩ ∅ =
>>       ∅ ∪ ∅ =
>>
>>
>>
>>
>
> >

http://iridia.ulb.ac.be/~marchal/

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