Opposite of a numbers opposite

Question

Jane completes several example problems that ask her to find the opposite of the opposite of a number and for each example the result is a positive number. Jane concludes that when she takes the opposite of the opposite of any number the result will always be positive. Is Jane correct why or why not?

Answer 1

She is not correct.  Example: n = -2

 

The opposite of n is 

 

-n = -(-2) = 2

 

The opposite of the opposite of n is

 

-(-n) = (-1)²n = (1)n = n = -2

 

The opposite of the opposite of a negative number is just the negative number.  The examples must have all been positive numbers, which does not represent the range of possibilities.