In mathematics, division by zero is undefined. This means that expressions like [tex]\( \frac{9}{0} \)[/tex] (or any number divided by zero) do not have a meaning within the standard rules of arithmetic.
To understand why, consider the definition of division: dividing a number [tex]\(a\)[/tex] by another number [tex]\(b\)[/tex] (where [tex]\(b \neq 0\)[/tex]) means finding a number [tex]\(c\)[/tex] such that [tex]\(b \times c = a\)[/tex]. For example, [tex]\( 9 \div 3 = 3 \)[/tex] because [tex]\( 3 \times 3 = 9 \)[/tex].
However, if we try to apply this idea to dividing by zero, we encounter a problem. Suppose [tex]\( \frac{9}{0} \)[/tex] is some number [tex]\(c\)[/tex] such that [tex]\( 0 \times c = 9 \)[/tex]. No matter what value we choose for [tex]\(c\)[/tex], [tex]\( 0 \times c \)[/tex] will always be 0, not 9. Therefore, there is no number [tex]\(c\)[/tex] that can satisfy the equation [tex]\( 0 \times c = 9 \)[/tex].
As a result, division by zero is not defined and is considered an invalid operation in mathematics.
