On 15 Jul 2009, at 09:09, Kim Jones wrote:

>
>
> On 14/07/2009, at 6:40 PM, Bruno Marchal wrote:
>
>> 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.
>>
>
>
>
> Quick (silly) questions:
>
> 1.
>
> why do you have to write "\inter"  ? Why not just write "inter"  ?
>
> Typing "\" causes me to make use of a key on my keyboard I have never
> used before which is scary ;-)

For the intersection of two sets S1 and S1,  I have used

1)  S1 ∩ S2

But the math symbol "∩"  did not go through all emailing system, so,  
I have used

2) S1 INTERSECTION S2

But then I recall that in mails, capital letters seems aggressive,  
loudly ..., so I have used

3) S1 intersection S2

But then the difference between what is supposed to be represent a  
mathematical symbols, and a word in english, disappears, so I have used

4) S1 \intersection S2

But this, on the last post, seems to me to be a little too long, and  
so I am using now

5) S1 \inter S2

Only God knows what I will use tomorrow. You should learn that there  
is no standard of mathematical notations, and no two mathematicians  
use the same symbols, and not one mathematician use the same symbols  
in two different texts. What is nice, is that, usually, mathematicians  
quickly redefine what they mean by any symbols at the beginning of  
their books and papers.
Of course doing math on mails aggravates apparently this search for  
the symbols which could satisfy everyone.

Sorry to scare you,

>
> 2.
>
> "such-that" is surely "such that" but the hyphen might just mean
> something
> (this is mathematics; there are dots and dashes and slashes all over
> the place so you have to know what they all mean)
>
> likewise
>
> "belongs-to" would still mean the same thing if we wrote "belongs to"
> would it not?

Same remark. I should have use \such-that, and \belongs-to.

Note that at this stage it is really not important to be aware of the  
difference between a symbol and what the symbols refer too, but in  
logic such differences acquire some importance at some point, and I  
just try to prepare you for such nuances, having the sequel of this  
introduction in my mind.

You question are not silly and makes sense, as you see,

Bruno


http://iridia.ulb.ac.be/~marchal/




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