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/ --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---