I have been thinking about equal signs lately (The subject of a forthcoming blog entry) and decided to see what Wolfram|Alpha thought. Here is my first try.
If you give Wolfram|Alpha an equation like without instructions, it responds with the statement “True”. Essentially it tries to prove an identity and it makes a mistake. The equation is not defined for .
If you give Wolfram|Alpha the instructions to show or prove the same equation, you get a similar result, still incorrect.
If you give Wolfram|Alpha instructions to solve the same equality. You get the following.
This is also incorrect. Since the expression on the left is undefined for , “all values of x” are not solutions.
These questions don’t strike me as too sophisticated to ask Wolfram|Alpha. That fact the expression is undefined at is fundamental to our discussions when we introduce function domains in college algebra and plays a large part in the discussion of limits in calculus. I am disappointed.