# Re: The seven step series

```  ----- Original Message -----
From: Bruno Marchal
Sent: Tuesday, July 07, 2009 2:07 PM
Subject: Re: The seven step series```
```

On 07 Jul 2009, at 16:18, m.a. wrote:

Bruno,

corrections than from pondering the rules to the point where I confuse myself.
m.a.

Do you remember, I asked you to give me all the subsets of {1, 2}. That is,
all the sets which are included in {1, 2}. You gave me the correct answer:
those subsets are { }, {1}, {2}, {1, 2}. You see that the set {1, 2} has 2
elements, and 4 subsets. But then I asked to give me the set of all subsets of
{1, 2}.
{1, 2} has four subsets, and it is natural to make that many a one, by
considering *the* set of all subsets of {1, 2}. The answer is:

{{ }, {1}, {2}, {1, 2}}

Considering all subsets of a set is a rather important operation, which we
will meet more than one times in the sequel. Given its importance
mathematicians gave it a name. It is the power operation. Later I will be able
to explain why it is called power.
It is an UNARY operation, which means it applies on ONE set. (Intersection,
and union are BINARY operations, they need two sets to work on).

So (power x) = {y such-that y is included in x}, by definition.

For example:
(power {1, 2}) = {{ }, {1}, {2}, {1, 2}}

Here are the three promised exercises. Compute

(power {1}) = ? {{ }, {1}}
(power {1, 2, 3}) = ? {{ }, {1}, {2}, {3}}
(power { }) = ?   {{ }}

Bruno

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