In mathematics, division by zero is undefined. This means that any expression where a number is divided by zero does not produce a finite or meaningful result.
To understand why, consider the nature of division. Division is essentially finding how many times a number (the divisor) fits into another number (the dividend). For example, [tex]\( \frac{8}{2} = 4 \)[/tex] because 2 fits into 8 exactly four times.
However, when zero is the divisor, we face a fundamental problem. The concept of how many times zero fits into any number doesn’t make sense, since multiplying zero by any number always results in zero, not in the original non-zero dividend.
This inconsistency makes it impossible to define a meaningful result for a division by zero. Therefore, we conclude that:
[tex]\[ \frac{-8}{0} \][/tex]
is undefined.
