Division by zero

For two real numbers $a$ and $b$ if we can find a unique real number $c$ such that $a = b \times c$ then we say $\frac{a}{b} = c$ and that is the definition of division. A division between real numbers is undefined if we fail to find any $c$ or there are more than one choices for $c$ . These may happen when $b = 0$ .

For example, $\frac{3}{0} = x$ would be defined if there is a unique real number $x$ such that $3 = 0 \times x$ . There is no such $x$ when multiplied by $0$ would give $3$ . So, $\frac{3}{0}$ is undefined.

For $\frac{0}{0} = y$ on the other hand, we have too many choices for $y$ since $0 = 0 \times y$ is true for any real number $y$ . As a result, $\frac{0}{0}$ is undefined as well.