November 24th, 2010, 10:46 AM  #1 
Joined: Nov 2010 Posts: 46 Thanks: 0  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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