Unique Subset of Set of FractionsDate: 7/19/96 at 16:20:48 From: Anonymous Subject: Unique Subset of Set of Fractions Is there a method or theory which I can use to determine a set of fractions such that if I add any subset of those fractions, I get a result that is unique relative to the result of any other subset in this set? Date: 7/22/96 at 15:45:52 From: Doctor Ceeks Subject: Re: Unique Subset of Set of Fractions Hi, There are various combinatorial theories which deal with issues related to the question you ask. However, your problem can be solved by considering the set of number 1/2, 1/4, 1/8, ..., 1/2^n. This is a set of n numbers whose subsets are distinguished by the sum of the elements they contain. This can be most easily seen if you interpret the sum in binary. There are 2^n subsets of any set of n elements, and the various sums of the elements in a subset of the above set range over binary numbers with n digits, from 0 to 1-1/2^n in increments of 1/2^n. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/25/96 at 0:22:20 From: Anonymous Subject: Re: Unique Subset of Set of Fractions Excellent, and thanks! bcp |
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