Unformatted text preview: b1 )1 = a1 Â· 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 ) = Â± p ( x ) q ( x ) : p ( x ) ,q ( x ) are polynomials, and q ( x ) 6 = 0 Â² 1 . Show that R ( x ) is a ï¬eld. 1 Notice that there is a diï¬€erent 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 âˆˆ R ( x ), while the former: p ( x ) is nonsense. 1...
View
Full Document
 Fall '10
 StevenKlee
 Calculus, Addition

Click to edit the document details