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November 24th, 2010, 10:46 AM   #1
 
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Summation

Let B be a finite subset of the set of real numbers and let b1,b2,...,bn be the elements of the set B. If F:{1,2,...,n}-->{1,2,...,n} is a bijective function, then by using also the commutative property of real numbers (a+b=b+a for every a,b?R) is been proved that b1+b2+...+bn=bF(1)+bF(2)+...+bF(n).
Thus we can represent the sum b1+b2+...+bn as ?b?Bb.
Proof (by mathematical induction) that for A,B two finite subsets of the set of real numbers with A?B=? that ?x?A?Bx=?a?Aa+?b?Bb.
Sorry if I have grammar mistakes (I'm from Greece).
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