My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 10th, 2013, 08:51 PM   #1
Member
 
Joined: Sep 2012

Posts: 69
Thanks: 0

proof involving real number!

Question
Let x be a positive real number. Prove that if , then .
(a) a direct proof
Assume is true. Then,



Since and , is positive real number. If x is less than or equal to 2, then . Therefore, . Q.E.D

Any comment?? And can anyone prove this by contrapositive?? Thanks.
eChung00 is offline  
 
March 10th, 2013, 10:30 PM   #2
Senior Member
 
Joined: Feb 2013

Posts: 281
Thanks: 0

Re: proof involving real number!

Correct. Maybe you should have stated the reason for x(x-2)<=2.

Anyway. x^2-x = (x-1/2)^2 - 1/4
you can wtite
(x-1/2)^2 > 9/4
i.e.
x>2

As we can see the (in)equality x-2/x ? 1 is logically the same than x ? 2.
csak is offline  
March 12th, 2013, 03:41 PM   #3
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: proof involving real number!

Contrapositive: If then so .
HallsofIvy is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
involving, number, proof, real



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Probability Involving Possible Outcomes of making a number. rnck Advanced Statistics 6 July 1st, 2013 07:21 AM
Problems involving number bases Michaeld71 Algebra 3 November 25th, 2012 04:17 PM
Finding real number in complex number TsAmE Complex Analysis 1 October 18th, 2010 05:38 PM
Proof involving cos and sin RastaMasta Algebra 3 October 20th, 2009 01:25 PM
Proof involving congruence!! eChung00 Applied Math 3 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.