319ISOL - MAT 319 SPRING 2008 MIDTERM I WRITE YOUR NAME...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
MAT 319 SPRING 2008 MIDTERM I !!! WRITE YOUR NAME, STUDENT ID BELOW !!! NAME : ID : THERE ARE SIX (6) PROBLEMS. THEY HAVE THE INDICATED VALUE. SHOW YOUR WORK!!! DO NOT TEAR-OFF ANY PAGE NO CALCULATORS NO PHONES ON YOUR DESK: ONLY test, pen, pencil eraser. 1 40pts 2 40pts 3 40pts 4 50pts 5 40pts 6 40pts Total 250pts 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 !!! WRITE YOUR NAME, STUDENT ID AND LECTURE N. BELOW !!! NAME : ID : LECTURE N. 1. Prove that the number 3 12 is irrational. Solution. By contradiction, assume 3 12 = r/s , where r, s are coprime natural numbers. We get 12 s 3 = r 3 . Then 2 divides r, so that r = 2 r 1 . We get 2 2 · 3 s 3 = 2 3 r 3 1 . We get 3 s 3 = 2 r 3 1 , so that 2 divides s. This contradicts r, s coprime.
Background image of page 2
3 2. In each case provide an example or state that it is not possible to do so and explain why. 2a Give one example of a countable set that is not finite. 2b Give one example of a countable set that is not denumerable.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/31/2011 for the course AMS 319 taught by Professor Mark during the Fall '10 term at SUNY Stony Brook.

Page1 / 11

319ISOL - MAT 319 SPRING 2008 MIDTERM I WRITE YOUR NAME...

This preview shows document pages 1 - 4. Sign up to view the full document.

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