Summation

Math Help on Cosine (cos), Sine (sin), Tangent (tan), Cotangent (cot), Cosecant (cosec), Secant (sec), Arccos, Arcsin, Arctan, Hypotenuse, Angles, Formulas, Trigonometric Circle, Unit Circles, Quadrants, Rotations; Triangles, Rectangles, Squares, Parallelograms, Quadrangles, Lozenges, Lines, Perpendicular, Parallel, Perpendicular, Parallel Lines, Bisector, Median, Gravity Center, Circumcenter, Circles, Pythagorean Theorem, Thales, Height, Side, Length, Ruler, Compass, Constructions, Formulas; Quadratic equations (Second degree equations), Absolute Values, Inequalities; Events, Random, Mean, Variance, Expectation, Wins, Losses, Bernoulli, Newton's Binomial Formula, Multinomial Formula, Tests, Samples on My Math Forum.

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 Σb∈Bb.
Proof (by mathematical induction) that for A,B two finite subsets of the set of real numbers with A∩B=∅ that Σx∈A∪Bx=Σa∈Aa+Σb∈Bb.
Sorry if I have grammar mistakes (I'm from Greece).
talisman
Jack of Clubs

Posts: 46
Joined: Wed Nov 24, 2010 1:29 pm