2
$\begingroup$

How can one tell the difference when the result is undefined or math just doesn't know how to provide a value for that particular equation? (the value still exists however)

For example, how could one prove that by definition division by zero is undefined; it's not that math doesnt' know the value, the value just doesn't exist.

  • 1
    What does it mean for “math” to know a value? Anyway, you can’t _prove_ something is undefined. For something to be undefined just means that we haven’t defined what it should be. In the case of division by zero, if we consider the set $\mathbb{R}$ of real numbers, there is no “natural” value in $\mathbb{R}$ that we could define $1/0$ to be.2012-06-21

3 Answers 3