
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 10th, 2013, 07:51 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. 
March 10th, 2013, 09:30 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(x2)<=2. Anyway. x^2x = (x1/2)^2  1/4 you can wtite (x1/2)^2 > 9/4 i.e. x>2 As we can see the (in)equality x2/x ? 1 is logically the same than x ? 2. 
March 12th, 2013, 02:41 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: proof involving real number!
Contrapositive: If then so .


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 06:21 AM 
Problems involving number bases  Michaeld71  Algebra  3  November 25th, 2012 03:17 PM 
Finding real number in complex number  TsAmE  Complex Analysis  1  October 18th, 2010 04:38 PM 
Proof involving cos and sin  RastaMasta  Algebra  3  October 20th, 2009 12:25 PM 
Proof involving congruence!!  eChung00  Applied Math  3  December 31st, 1969 04:00 PM 