In mathematics, we can either prove or disprove a statement.  When a statement is true, we have to prove that, in general, it is always true.  On the contrary, when we disprove a statement, it suffices to show that the statement is not true for just one case.

For example, if I say “When we add two numbers the answer is always greater than each of the two numbers we start from”, it suffices to say “No this is not true, for example 3 + 0 is equal to 3, which is not greater than the original separate numbers.”  Such an example is called a counterexample. Three other arithmetic myths include:

1) Multiplying two numbers yields a number greater than the original numbers. False: -3 times 4 is a counterexample;

2) The square of a number is larger than the original number. False: try squaring 0.5;

3) The square root of a negative number does not exist. False: the square root of -4 is 2i, it exists as an imaginary number.

These myths usually result from the fact that, as we start learning mathematics from an early age, we are exposed to a restrictive set of numbers, namely the natural numbers (positive whole numbers).

The rules which are true for these particular numbers are not true for all real and non-real (complex) numbers.