Question

Disprove the following statement by giving a counterexample. A counterexample is a specific case that shows a statement is false. Explain.

Every real number has a multiplicative inverse.

Short answer

0 is the real number which does not has a multiplicative inverse.

Step-by-step solution

- Define real number

Combine sets of rational and irrational number is real number.

- Define multiplicative inverse

Let a be the real number such that $a·\frac{1}{a}=1$then $\frac{1}{a}$ is the multiplicative inverse of a

- Write counterexample

As, 0 is a real number but there does not exist a number of the form $\frac{1}{0}$

So, 0 does not has a multiplicative inverse.

Thus, every real number does not has a multiplicative inverse.