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Unformatted text preview: Notation and Terminology 1. R : The symbol R denotes the set of real numbers together with usual real number arithmetic. The distance between two numbers x and y is the absolute value of their difference:  x y  . 2. R n : For each positive integer n the set R n is the collection of all ordered ntuples of real numbers: R n = { ( x 1 ,...,x n )  x k ∈ R for k = 1 , 2 ,...,n } . So x ∈ R n means x = ( x 1 ,x 2 ,...,x n ) for some real numbers x 1 , x 2 , ..., x n . The entry x k is called the kth component of x . The distance between two points x = ( x 1 ,...,x n ) and y = ( y 1 ,...,y n ) from R n is denoted by k x y k and defined by k x y k := v u u t n X k =1 ( x k y k ) 2 . When x ∈ R 1 then x has just one component x = ( x 1 ) and order is not an issue. We represent this 1tuple simply as a real number x . When n = 1 the above definition of distance is consistent because, for x,y ∈ R 1 , k x y k = p ( x y ) 2 =  x y  ....
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This document was uploaded on 09/22/2011.
 Spring '09

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