Question

What is a counterexample to this claim? Dividing a number by 2 always results in a smaller number.

Answer 1

Given:

Dividing a number by 2 always results in a smaller number.

To find:

The counterexample to the given claim.

Solution:

If 0 is divided by is divided by any non-zero real number $a$, then

$\dfrac{0}{a}=0$

Let us consider the unknown number be 0. Then dividing a number by 2, we get

$\dfrac{0}{2}=0$

Here, the result is not a smaller number because $0=0$.

Therefore, the counterexample to the given claim is "Dividing 0 by 2".