My Math Forum What is the cardinality of each of the following sets?

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 November 4th, 2012, 03:49 AM #1 Member   Joined: Jun 2010 Posts: 35 Thanks: 0 What is the cardinality of each of the following sets? What is the cardinality of each of the following sets? a) $\varnothing$ b) ${\varnothing}$ c) ${\varnothing,{\varnothing}}$ d) ${\varnothing, {\varnothing}, {\varnothing, {\varnothing}}}$ Please include explanations for each of your replies. Thanks.
 November 4th, 2012, 02:29 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 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.
 November 4th, 2012, 09:14 PM #3 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 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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