Algebra I: Find a counter-example or otherwise disprove a conjecture
This is a free lesson from our course in Algebra I
 
   
In this lesson, you'll learn how to use the counter example to disprove a conjecture. A conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. Once the conjucture is proven, it is known as a theorem and and joins the mathematical facts. The counter-example, like mentioned above, can be used to disprove a mathematical conjecture.For example:
  • all prime numbers are odd (conjecture)
  • but 2 is prime number (counter example)
  • the counter example above disproves the conjecture, hence we can conclude that not all prime numbers are odd.
(More text below video...)
<h2>Algebra I - Find a counter-example or otherwise disprove a conjecture</h2> <p>logical reasoning, counter, example, conjecture, theorem, prove, statements, counterexample, define, conclude, conjectures, disprove, prime, numbers, practice questions, quizzes, solution</p> <p>A conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove.</p>
Other useful lessons:
Inductive vs. Deductive reasoning
Hypothesis and conclusions of an argument
(Continued from above) Let's look at one more example:
Prove that “For every positive integer n, n! <= n2.”
Start testing some cases say, n = 1, 2, 3 etc.
It might seem like it is true for some cases but how far do you test, say n = 4.
Here, you get n! = 24 and n2 = 16 which is a counter example for this theorem. Hence,even finding a single case that doesn’t satisfy the condition is enough to disprove the theorem.
Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
- All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic.
- We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the problem-solving process!
- Winpossible courses have been used by students for help with homework and by homeschoolers.
- Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.
 
       
     
 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version