Looking through the logs as to the search terms that come up with the real analysis notes, I noticed several hits that came from google searches where the person simply typed in a problem word for word looking for a solution. For example: In advanced Calculus 1, define f:R converges to R by f(x)= 8x if x is rational and f(x)= 2x^2+8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1. This is exactly the search phrase someone used to find the notes.
I wonder if the person really thought that this exact problem and its solution would appear on the web? In a way it is sad that the person doesn’t try to think. Fortunately this exact problem is very unlikely to have an exact solution on the web somewhere (it is a well designed problem for the google age). Hopefully the person will now have to start using the brain.