Consider the equation

What is x? Well:

I'm a physicist, not a mathematician. In physics, we always check our result; is it reasonable? Let's do it here:

Well, here's the problem... Is 2 truly a solution to the equation? If we take a look at the limit of the left-hand expression as

, it supports that x is a solution:

When we take this limit, the expression is determined to be 4; hence 2 is a solution to the equation at the top. As we have seen though,

isn't working very well in practice. So, the big questions:

Is it mathematically correct to say that 2 is a solution to the equation?

- If the answer is yes, doesn't it create a problem that the left-hand side turns out to be

, when we are calculation something that can be expressed by this equation?