Question 698728: Yes, Hi. I need to show the conjecture is false by finding a counterexample in the following statement:
The product of any two consecutive integers is positive.
Thank you.
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! A counterexample is any example of two numbers which shows the statement is false. Here, that is a set of integers that results in a product that is not positive. For this problem, remember that the product of any number times 0 equals 0. Since 0 is an integer, and it is not positive, if 0 is one of the numbers the product will not be positive.
-1 and 0 is one such counterexample. 0 and 1 is another. I think these are the only two counterexamples, since the product of two negative numbers is positive, and the product of two positive numbers is positive.
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