notation - Notation and Terminology 1. R : The symbol R...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 n-tuples 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 k-th 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 1-tuple 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 | ....
View Full Document

This document was uploaded on 09/22/2011.

Ask a homework question - tutors are online