Find a counter-example or otherwise disprove a conjecture

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...)

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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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