Test_3 - Numbers and Polynomials Test 3 Answer FOUR...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Numbers and Polynomials Test 3 Answer FOUR questions. Be sure to give reasons for each step. 1. Where possible, in each case give (with justification) an example of a nonempty set of real numbers that is bounded above and has: (i) a greatest element; (ii) a least upper bound but no greatest element; (iii) no least upper bound. 2. Let A be a nonempty subset of N that is bounded above (by a real number). Show that its least upper bound lub A is an element of A . 3. Let P : = R \ Q denote the set of all irrational real numbers. For A, B R let A + B : = { a + b : a A, b B } . Identify each of the following subsets of R : (i) Q + Q ; (ii) Q + P ; (iii) P + P . 4. Let p be a prime number and let a, b Q . Show explicitly (and carefully: attend to the denominator) that if a + b p is nonzero then there exist x, y Q such that 1 / ( a + b p ) = x + y p . 5. Let p be a prime number and n a positive integer. Show that if n Q [ p ] and n is not the square of an integer then
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/12/2011 for the course MAS 3300 taught by Professor Staff during the Fall '08 term at University of Florida.

Page1 / 2

Test_3 - Numbers and Polynomials Test 3 Answer FOUR...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online