This preview shows page 1. Sign up to view the full content.
Unformatted text preview: b1 )1 = a1 b 2.2: Is the following statement true or false? If x , y , and z are irrational numbers, then x + y + z is irrational. ( Hint: You did some homework last week. One of the problems may be useful!) 2.3 Let R ( x ) denote the collection of rational functions : R ( x ) = p ( x ) q ( x ) : p ( x ) ,q ( x ) are polynomials, and q ( x ) 6 = 0 1 . Show that R ( x ) is a eld. 1 Notice that there is a dierent between q ( x ) = 0, which is the function whose output is 0, independently of the input value x ; and a polynomial function like q ( x ) = x 2 + 2 x3, which has zeros (x=3,1), but is not identically equal to 0. The latter is perfectly valid: 1 x 2 +2 x +1 R ( x ), while the former: p ( x ) is nonsense. 1...
View
Full
Document
This note was uploaded on 03/18/2012 for the course MAT MAT 25 taught by Professor Stevenklee during the Fall '10 term at UC Davis.
 Fall '10
 StevenKlee
 Calculus, Addition

Click to edit the document details