document.write( "Question 475954: for each given set,how do I choose the set with the same cardinality\r
\n" ); document.write( "\n" ); document.write( "{1,4,7,...,91,94}
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\n" ); document.write( "{1,2,3,...,205,206} \r
\n" ); document.write( "\n" ); document.write( "{1,3,5,...,211,213}
\n" ); document.write( " possible choices {147,148,149,...,240}{131,132,133,...,247} {3,4,5,...,34} {1423,1425,1427,...1833} \n" ); document.write( "

Algebra.Com's Answer #326385 by richard1234(7193) $\"\"$ $\"About$

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There are two ways to find the cardinality of this set. You can either use the formula for an arithmetic sequence a_n = a_1 + (n-1)d, but I prefer finding the cardinality by doing a series of transformations on the set. For example, with the set {1,4,7,...,94} we can add 2 to each element (this will not affect cardinality) to get {3,6,...,96}, then divide each element by 3 to get {1,2,...,32} which obviously has 32 elements. \n" ); document.write( "

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