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November 4th, 2012, 03:49 AM   #1
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What is the cardinality of each of the following sets?

What is the cardinality of each of the following sets?

a)

b)

c)

d)

Please include explanations for each of your replies. Thanks.
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November 4th, 2012, 02:29 PM   #2
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Re: What is the cardinality of each of the following sets?

It's hard to figure out what you are saying but I think you mean:
a: { }
b: { { } }
c: { { }, { } }
d: { { }, { }, { }, { } }

Do you know the definition of "cardinality of set"? If you do these should be easy.
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November 4th, 2012, 09:14 PM   #3
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Re: What is the cardinality of each of the following sets?

Think of a set as an empty sack where you can insert anything you want, including OTHER empty sacks. Whatever you insert becomes an element of the set, If you do not insert anything, then it is the empty set.

a: just an empty sack
b: an empty sack inside a sack, so the OUTSIDE sack is not empty...it contains 1 element.

You see?

A follow up question may be

what is the cardinality of { { { } } }

?

The outside sack has 2 sacks within it, but one empty sack is within the other and that is within the third. So, is the cardinality of the outside sack 2 or 1 ?

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