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/ > > > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---