SCIENCE AND MATH Why Can't You Divide a Number by 0?

by Maxwell Lin

Most of us are taught at an early age that you can’t subtract a larger number from a smaller one. However, we are taught later on that negative numbers exist. However, we are also taught to never divide by zero. But why can’t you divide by zero?

Well, it’s much more complicated than you might think There are a few cases to consider A common misconception about dividing by zero is that anything divided by zero is infinity, because it is impossible to make a larger number than zero by multiplying it by real numbers. Therefore, you need a number infinitely large to achieve this feat. However, this conception is extremely flawed, for a number of reasons.

First, let’s assume that this expression is true: 1÷0=∞ In order to undo this division by zero, you must multiply both sides of the equation by zero. However, what is infinity times zero? Well, it is undefined. And that means our discussion ends here, because undefined, well, is undefined. However, we can also assume two other things. If zero times infinity is infinity, then you get the statement that 1=∞, which obviously doesn't look right. Also, if you assume that zero times infinity is zero, then you get the statement that 1=0, which looks even more wrong, and if either of these equations were true, everything we knew about mathematics would come crashing down. Also, there’s the misconception that 1 divided by zero is zero. But that’s just wrong, because that eventually ends up in the 1=0 equation, and you already know that that means.

Second, dividing a number by x is the same as multiplying that number by the multiplicative inverse of x, which is always ¹⁄ₓ So if we want to divide by zero, we can also multiply by ¹⁄ₒ