None of this has anything to do with limits. The answer is also not infinity, so stop saying that people. Infinity is not a number.
Let me explain something about solutions to linear equations. There are three possible sizes for a set of solutions to an equation: Either no solutions, one solution, or infinitely many solutions. When there is exactly one solution, we say the relation is well-defined; when there are no solutions or infinitely many solutions, the relation is undefined.
Let me give you an example for each:
2*x=6 <- There is only one solution: x=3.
1*x=6 <- There are no solutions, because no matter what value for x you put, this equation will never be true.
1*x=1 <- There are infinitely many solutions, because any number for x makes this equation true.
The reason we say the first solution is well-defined is because we can just write it: x=3. x has exactly one possible value.
The reason we say the last two are undefined is because we can't just write x=something; there isn't one something. You have to express the answer in terms of sets. The solution set of x=1/1 is everything, or {x|xeR}, whereas the solution set of x/1 for x!=1 is the empty set.