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Unique Subset of Set of Fractions

Date: 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


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
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Date: 7/25/96 at 0:22:20
From: Anonymous
Subject: Re: Unique Subset of Set of Fractions

Excellent, and thanks!

Associated Topics:
High School Permutations and Combinations
High School Sequences, Series

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