Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Find a Counterexample


Date: 8/29/96 at 11:5:51
From: Nina Morgan
Subject: Find a Counterexample

What is a counterexample of:

If a>b and b=5, then a >= 6.


Date: 8/29/96 at 11:26:45
From: Doctor Mike
Subject: Re: Find a Counterexample

Hi Nina,

  I can give you a counterexample, sort of.  If a is any number
between 5 and 6, for instance 5.5 , then a is greater than 5
but a is not >= 6.  Another counterexample is 5.4321 and
another is 17/3 .  

These both can be written as fractions. A couple of counterexamples 
that can't are "the square root of 33" and "2*pi - 1" where pi is the 
famous number 3.1415926535898......

Of course, there is an unlimited supply of others.
  
So why did I say sort of?  Because I wasn't completely sure of the 
background of the problem.  If this statement was given in the 
environment of whole numbers (also called natural numbers or counting 
numbers or integers) then none of my fine counterexamples does the 
job.  That is because the only integers greater than 5 are 6, 7, 8, 9, 
10, etc.  It certainly is true about all of these that they are 
greater than or equal to 6, so if we are talking about integers, there 
is no counterexample. 
  
I hope this helps.  Write back if you have other questions.  

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/