On 02 Jun 2009, at 22:00, Brent Meeker wrote:

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>
> Bruno Marchal wrote:
>> ...
>> 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?
>> 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?
>>
>
> But there are no duplicates in sets; so {6,6,6} is either not a set
> (instead it's a triple) or it's just strange notation for {6}. Right?
Right. I was not well inspired with this exercise. At least it should
have been given AFTER having said that a set is determined only by its
elements. So {6, 6, 6} is really the same as the set {6}. Something
like {6, 6, 6} is usually called a bag, and will never been used.
Of course {666} is different from {6}.
Apology. This will probably happen again, when I am distracted, so if
an exercise seems weird or senseless, please don't panic!
Bruno
http://iridia.ulb.ac.be/~marchal/
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