Find a CounterexampleDate: 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/ |
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