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.
>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}?


>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,  
>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}?


>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, ...}.


>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!



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