which function is undefined for x = 0?

It’s the function that counts as undefined. This is about the way things are defined, a little bit about how a function is defined, and how you can be certain the function does what it says it is doing.

x = 0 is a function (or an operator) that we can be certain is undefined when it is called with only a value of zero. This is a big one for us, which is why we have a function like isDefinitelyNull. The idea is that we can be certain that an expression is undefined when it is not used with a value of zero. I use this often when working with complex mathematical functions.

We can also be certain that an expression is undefined when it is used with a value of zero, but not when it is used with a value of nonzero. x 0 is an example for this. The expression x 0 is not used with a value of zero, but it is used with a value of nonzero. This is useful in a number of ways.

If you know that the expression is undefined for x = 0, but you don’t know that it is undefined for x!= 0, then x!= 0 can be a valid solution.

For instance, it is undefined for x = 0 but not for x = 10. Using the former as the first-case solution, then x 10 is always a valid solution. This makes it especially clear how to resolve the ambiguous expression x = 0.

However, we can also use the second-case solution to solve the ambiguous expression x 0. We know that x 0 is undefined for x 0, so we know that x 0 is not a valid solution.

Similarly, we can use the first-case solution to solve the ambiguous expression x 0. We know that x 0 is undefined for x 0, so we know that x 0 is not a valid solution.

This is one of those situations where it’s easiest to just use the second case and solve the ambiguity.

You can always use the second case if you find yourself in the same situation. However, we also need to be aware of the fact that x 0 is undefined for x 0, so we don’t need to use the first case.