document.write( "Question 1106507: If A={5,3,3,7} List all the subsets of A set. \n" ); document.write( "

Algebra.Com's Answer #721504 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "This post has a pitfall: the list of elements contains two identical names.\r
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\n" ); document.write( "\n" ); document.write( "There is nothing criminal or fatal in it: you can meet such cases in Math or even in real life.\r
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\n" ); document.write( "\n" ); document.write( "        For example, if a polynomial has multiple roots, then the list of the roots may contain identical numbers.\r
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\n" ); document.write( "\n" ); document.write( "        Or a human family may have TWINS.     // But even then the parents give different names to the children . . . (as a rule).\r
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\n" ); document.write( "\n" ); document.write( "        Or a list of voters can contain identical names, when they relate to different people.\r
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\n" ); document.write( "\n" ); document.write( "        As well as the list of people/abonents in a telephone book . . . \r
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\n" ); document.write( "\n" ); document.write( "But, in such cases, if the author of a mathematical text (including the person who originated this post/(posted text))
\n" ); document.write( "wants to be mathematically correct, he (or she) must explain WHY he (or she) did include two (or more) identical names
\n" ); document.write( "in the element list of the set.     A good style and a common sense requires it . . . \r
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\n" ); document.write( "\n" ); document.write( "If such an explanation is absent, then BY DEFAULT the identical names are considered as describing
\n" ); document.write( "the presence of different elements (different \"copies\") in the set. \r
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\n" ); document.write( "\n" ); document.write( "After this PREFACE, read my response to your problem. \r
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document.write( "    List AS MANY subsets as you can ON YOUR OWN.\r\n" );
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document.write( "    Then post your results to the forum.\r\n" );
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document.write( "    We will check it.\r\n" );
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document.write( "    Together with the empty subset and with the improper subset (which coinsides with the given set) the total number of subsets \r\n" );
document.write( "    in this case is  = 16.\r\n" );
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\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - How many subsets are there in a given finite set of n elements?\r
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