# Re: The seven step-Mathematical preliminaries

```Excellent!

Kim, are you OK with Marty's answers?```
```
Does someone have a (non philosophical) problem?

I will be busy right now (9h22 am). This afternoon I will send the
next seven exercises.

Bruno

On 02 Jun 2009, at 21:57, m.a. wrote:

> Bruno,
>             I appreciate the simplicity of the examples. My answers
> follow the questions.    marty a.
> ----- Original Message -----
> From: "Bruno Marchal" <marc...@ulb.ac.be>
>
> >
> >
> > ============================================= begin
> > ===============================
> >
> > 1) SET
> >
> > Informal definition: a set is a collection of object, called
> elements,
> > with the idea that it, the collection or set, can be considered
> itself
> > as an object. It is a many seen as a one, if you want. If the set is
> > not to big, we can describe it exhaustively by listing the elements,
> > if the set is bigger, we can describe it by some other way.
> Usually we
> > use accolades "{", followed by the elements, separated by commas,
> and
> > then "}", in the exhaustive description of a set.
> >
> > Example/exercise:
> >
> > 1) The set of odd natural numbers which are little than 10. This
> is a
> > well defined, and not to big set, so we can describe it
> exhaustively by
> > {1, 3, 5, 7, 9}. In this case we say that 7 belongs to  {1, 3, 5,
> 7, 9}.
> > Exercise 1: does the number 24 belongs to the set {1, 3, 5, 7,
> 9}?    NO
> >
> > 2) the set of even natural number  which are little than 13. It is
> {0,
> > 2, 4, 6, 8, 10, 12}. OK? Some people can have a difficulty which is
> > not related to the notion of set, for example they can ask
> themselves
> > if zero (0) is really an even number. We will come back to this.
> >
> > 3) The set of odd natural numbers which are little than 100. This
> set
> > is already too big to describe exhaustively. We will freely describe
> > such a set by a quasi exhaustion like {1, 3, 5, 7, 9, 11, ... 95,
> 97,
> > 99}.
> > Exercise 2: does the number 93 belongs to the set of odd natural
> > numbers which are little than 100, that is: does 93 belongs to {1,
> 3,
> > 5, 7, 9, 11, ... 95, 97,
> 99}?                                                               YES
> >
> > 4) The set of all natural numbers. This set is hard to define, yet I
> > hope you agree we can describe it by the infinite quasi exhaustion
> by
> > {0, 1, 2, 3, ...}.
> > Exercise 3: does the number 666 belongs to the set of natural
> numbers,
> > that is does 666 belongs to {0, 1, 2,
> 3, ...}.                                         YES
> > Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,
> >
> 3
> , ...}?
>                        NO
>  (a guess)
> >
> >
> > 5) When a set is too big or cumbersome, mathematician like to give
> > them a name. They will usually say: let S be the set {14, 345, 78}.
> > Then we can say that 14 belongs to S, for example.
> > Exercise 5: does 345 belongs to
> S?                                                    YES
> >
> > A set is entirely defined by its elements. Put in another way, we
> will
> > say that two sets are equal if they have the same elements.
> > Exercise 6. Let S be the set {0, 1, 45} and let M be the set
> described
> > by {45, 0, 1}. Is it true or false that S is equal to
> M?                              YES
> > Exercise 7. Let S be the set {666} and M be the set {6, 6, 6}. Is is
> > true or false that S is equal to
> M?                                                        NO
> >
> > Seven exercises are enough. Are you ready to answer them. I hope you
> > don't find them too much easy, because I intend to proceed in a way
> > such that all exercise will be as easy, despite we will climb toward
> > very much deeper notion. Feel free to ask question, comments, etc. I
> > will try to adapt
> myself
> .                                                                       SO
>  FAR SO GOOD
> >
> > Next: we will see some operation on sets (union, intersection), and
> > the notion of subset. If all this work, I will build a latex
> document,
> > and make it the standard reference for the seventh step for the non
> > mathematician, or for the beginners in mathematics.
> >
> > Bruno
> >
> >
> >
> > http://iridia.ulb.ac.be/~marchal/
> >
> >
> >
> >
> >
> >

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

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