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July 15th, 2014, 12:13 AM   #1
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On why it does not matter

I'm reading a very basic introduction to sets and it gives the following RULES:

Rule 1. An element is listed only once..so x, x, y, z is {x, y, z}

Rule 2. Order of the elements in the list does not matter so {a, b, c} = {b, c, a}

Are these rules arbitrary or do they have a reason?

I can think of a set where each instance of an element is important e.g. height of 3 people can be {5, 5, 6}. Here the two occurrences of 5 are important to calculate the central tendency.
Why is it that each element in a set has to be unique?

Consider the set {1, 2, 3}. Here the numbers are increasing in a specific order and so {1, 2, 3} is not equal to {1, 3, 2}. If we say the two are equal, we are losing information.
Why is it that order of the elements is not important?

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July 15th, 2014, 06:30 AM   #2
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Originally Posted by shunya View Post
Are these rules arbitrary or do they have a reason?
The reason is to have standard terminology. If you care about order then you need to say "tuple" rather than "set". If you don't care about order, but you do care about multiplicity, then you need to say "multiset".
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July 15th, 2014, 08:56 PM   #3
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The reason is to have standard terminology. If you care about order then you need to say "tuple" rather than "set". If you don't care about order, but you do care about multiplicity, then you need to say "multiset".
Thanks CRGreathouse...you're great!
We do have different areas where the order and repetition are taken into consideration.
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July 16th, 2014, 06:31 AM   #4
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We do have different areas where the order and repetition are taken into consideration.
Yes. And in fact, you can build those objects out of sets!
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