I found this problem which Mathematica does not handle well, and I am wondering why. Here is the problem
f[x_] := Floor[x] + Floor[-x]
Limit[f[x], x->2, Direction -> 1]
Limit[f[x], x->2, Direction -> -1]
When evaluated I get: 0
Zero is not the limit of this function -1 is, jst look at the graph and you can see that as x approaches 2 it gets closer and closer (really stays contant) to -2. Whereas when f is evaluated I get 0, that is the right answer for f but not for the limit as f approaches 2. Any insights here?