Pamela A.

asked • 02/02/14

Are the sets equal?

{4,4,11,11,17}={4,11,17}

Pamela A.

I am getting toooo many different answers... I am taking contemporary math.... Not basic math. Hope that helps. I am not learning mean, median, and mode...
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02/02/14

Kenneth G.

Pamela,
 
A set is a collection of distinct objects.  The collection {4,4,1,1,17} does not have distinct objects.  Therefore it's not a set.  You can look up the definition of a set in mathematics on the internet.  Here is a link: http://en.wikipedia.org/wiki/Set_(mathematics) .     Two sets are equal if they have exactly the same elements.  That is, the set {11,4,17} is the same set as {4,11,17}.  Order is not important for a set.  A set cannot have two elements that are the same.  {4,4,1,1,17} is NOT a set.
 
 
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02/03/14

Vivian L.

Kenneth;
The Wikipedia article you cited all states that...
"Every element of a set must be unique; no two members may be identical. (A multiset is a generalized concept of a set that relaxes this criterion.) All set operations preserve this property.... Combining these two ideas into an example
{6, 11} = {11, 6} = {11, 6, 6, 11}"
(emphasis supplied)
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02/03/14

Kenneth G.

A Multiset is the same concept as a Collection.  But the problem above did not say anything about a multiset. The problem is about sets. 
 
 
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02/03/14

Kenneth G.

Multisets cannot be equal unless they have the same number of elements, so {6,11} would still NOT equal {11,6,6,11} even for Multisets. See http://www.proofwiki.org/wiki/Definition:Multiset which gives the definition of equality for Multisets.
 
 
 
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02/03/14

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Kenneth G. answered • 02/02/14

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Are the sets equal?
{4,4,11,11,17}={4,11,17}
====================================
 
A set has DISTINCT objects (reference: http://en.wikipedia.org/wiki/Set_(mathematics)).  So {4,4,1,1,17} is not a set.  It is a collection which does not have distinct objects.  Or you could say that the two objects are NOT equal because they are not the same kind of object - one is a collection and one is a set.
 
Therefore the question is not legitimate.
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Tiffany V. answered • 02/02/14

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Hello Pamela,
 
In order for two sets to be equal they must contain the same elements. An element is a unique value in this case. If a single value is repeated several times, it still only represents one element (the specific value). For example:
 
{a,a,b} = {a,b} = {b,a} = {b,b,b,a,a}
 
I hope that helps.
 
Tiffany
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Pamela A.

So this means that it is not equal right? Cause thats what Im getting from the example...
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02/02/14

Tiffany V.

Hi Pamela,
 
I would like to clarify the example. In the first set {a,a,b} there are 2 elements, a and b, it doesn't matter that a is there twice. In the second set {a,b} there are also 2 elements, a and b. The same is true for the 3rd and 4th set. They all have the same elements, a and b. That is the definition of equal sets, they must contain the same elements. So, in the example I have provided, all of the sets are equal because they contain the same elements, a and b. I hope that clears it up!
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02/02/14

Vivian L. answered • 02/02/14

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Hi Pamela;
{4,4,11,11,17}={4,11,17}
If we calculate mean, also known as average...
(47/5) does not equal (32/3).
If we calculate median, also known as middle value...
11=11
If we calculate mode, the number repeated most often...
(4 and 11) does not equal (4, 11 and 17).
 
This is why these sets are different.
 
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