On 15 Jul 2009, at 04:15, m.a. wrote:

> ----- Original Message -----
> From: Bruno Marchal
> To: everything-list@googlegroups.com
> Sent: Tuesday, July 14, 2009 4:40 AM
> Subject: Re: The seven step series
> Hi Kim, Marty, Johnathan, John, Mirek, and all...
> Bruno: May I advise you about an instance of English usage? The word  
> "supposed" in the next sentence is often used as sarcasm to imply  
> serious doubt about the statement. In this context it can be  
> interpreted as a slight. I think you meant to say "assumed" which  
> implies an evident fact. Please don't apologize, we are most  
> grateful for your efforts in using English and are happy to make  
> allowances for minor slips.
> B = {Kim, Marty, Russell, Bruno, George, Jurgen} is  a set with 5  
> elements which are supposed to be humans.

Thanks for letting me know. In french "I assume" is the same as "I  
suppose". I'm afraid it will take time for me not doing that error  
again. But don't hesitate to remind me of the "false friend" behavior.  
Sorry for the unintended sarcasm.
To be sure it is not really an assumption, and a "supposition" means  
more like an "obvious implicit fact we should take into account  
without mentioning", as opposed to an "assumption" which is more akin  
to "a key hypothesis". Here I was referring to conventions only, but  
then, as yopu point out, an non intended sarcasm could be see.  
Difficult. That is why I prefer to stick on less ambiguous, purely  
mathematical examples of sets.

> I also have a question: see below:
> We have seen INTERSECTION, and UNION.
> The intersection of the two sets S1 = {1, 2, 3} and S2 = {2, 3, 7,  
> 8} will be written (S1 \inter S2), and is equal to the set of  
> elements which belongs to both S1 and S2. We have
> (S1 \inter S2) = {2, 3}
> We can define (S1 \inter S2) = {x such-that ((x belongs-to S1) and  
> (x belongs-to S2))}
> 2 belongs to (S1 \inter S2) because ((2 belongs-to S1) and (2  
> belongs-to S2))
> 8 does not belongs to (S1 \inter S2) because it is false that ((2  
> belongs-to S1) and (2 belongs-to S2)). Indeed 8 does not belong to S1.
> Doesn't the statement in bold (above) contradict the statement  
> immediately preceding (also in bold)?

You are completely right. I just did a copy and past, and forget to  
substitute the "2" by the "8".

So the statements are:

2 belongs to (S1 \inter S2) because ((2 belongs-to S1) and (2 belongs- 
to S2))
8 does not belongs to (S1 \inter S2) because it is false that ((8  
belongs-to S1) and (8 belongs-to S2)).



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