goldch0 - Contents Mathematical Sign Language 1 0.A Numbers...

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Unformatted text preview: Contents Mathematical Sign Language 1 0.A Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.B Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.C Operations on Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.D Implication and Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.E Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.F Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.G Summation Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0.H Factorial Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0.I Binomial Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Mathematical Sign Language 0.1 Mathematical Sign Language Mathematical formulations should be precise and concise. To achieve this aim, mathematical language employs symbols and formulas. We review some basic notation in this chapter. 0.A Numbers Certain sets of numbers have their own symbol. R denotes the set of all real numbers , Q denotes the set of all rational numbers, i.e. all fractions p/q with p,q integers and q 6 = 0, Z denotes the set of all integers , N denotes the set of all natural numbers, these are the nonnegative integers. (Thus 0 is the smallest natural number.) ∅ denotes the empty set, the only set that contains no element. 0.B Intervals Intervals are special — and important! — subsets of the real numbers. They are solution sets to inequalities and come in various forms. The Open interval ( a,b ) is the set of real numbers { x ∈ R | a < x < b } , The Closed interval [ a,b ] is the set of real numbers { x ∈ R | a ≤ x ≤ b } , The Half-open interval ( a,b ] is the set of real numbers { x ∈ R | a < x ≤ b } , The Half-open interval [ a,b ) is the set of real numbers { x ∈ R | a ≤ x < b } , The Infinite interval [ a, ∞ ) is the set of real numbers { x ∈ R | a ≤ x } , The (Open) Infinite interval ( a, ∞ ) is the set of real numbers { x ∈ R | a < x } , The Infinite interval (-∞ ,b ] is the set of real numbers...
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This note was uploaded on 10/04/2011 for the course MATH 16121 taught by Professor Rachelbelinsky during the Spring '11 term at Georgia State.

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goldch0 - Contents Mathematical Sign Language 1 0.A Numbers...

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