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:
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all prime numbers are odd (conjecture)
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but 2 is prime number (counter example)
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the counter example above disproves the conjecture, hence we can conclude that not all prime numbers are odd.
(More text below video...)
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(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.
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