On Wed Jun 3 0:39 , Bruno Marchal <marc...@ulb.ac.be> sent: > >Hi Kim, Hi Marty and others, > >So it is perhaps time to do some math. It is >Obviously this is a not a course in math, but it is an explanation >from scratch of the seven step of the universal dovetailer argument. >It is a shortcut, and most probably we will make some digression from >time to time, but let us try not to digress too much. > >Kim, you are OK with this? I am I have to take into account the problem you >did have with math, and which makes this lesson a bit challenging for >me, and I guess for you too. Hopefully my innocence will allow me to bypass the pedantry and orthodoxies of the field and allow a shortcut to a high level of understanding of the UDA. Only a complete neophyte would have the gall to say something like that! > >I begin with the very useful and elementary notion of set, as >explained in what is called "naive set theory", and which is the base >of almost all part of math. > >============================================= 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 idea what square-root(2) means. When I said I was innumerate I wasn't kidding! I could of course look it up or ask my mathematics teacher friends but I just know your explanation will make theirs seem trite. > > >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? Clearly, 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? True - unless integer position within a given sequence in a set plays a role. I will guess that it does not >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? False - the commas separate each natural number > >Seven exercises are enough. Are you ready to answer them. Done - apart from the square root question 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. Very excited about doing this. If you can make it all as approachable as this I am over the moon! > >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. What a wonderful idea! Kim > >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 -~----------~----~----~----~------~----~------~--~---

- Re: The seven step-Mathematical preliminaries kimjo...@ozemail.com.au
- Re: The seven step-Mathematical preliminaries Brian Tenneson
- Re: The seven step-Mathematical preliminaries... Bruno Marchal
- Re: The seven step-Mathematical prelimina... m.a.
- Re: The seven step-Mathematical preli... Bruno Marchal
- Re: The seven step-Mathematical p... m.a.
- Re: The seven step-Mathemati... Bruno Marchal

- Re: The seven step-Mathematical p... m.a.
- Re: The seven step-Mathemati... Bruno Marchal
- RE: The seven step-Mathe... Jesse Mazer