What does the set {n | n is an integer and n = n + 1} represent? I am reading Michael Sipser's book Introduction to the Theory of Computation, which mentions the set $$S = \{ n \mid \text{$n$ is an integer and $n = n + 1$}\}.$$ This  doesn't make any sense to me.
I would understand if $n$ were equal to infinity or something, so it probably wouldn't matter if we added $1$ to it.
Am I understanding it correctly?
Or is this just an empty set?
But infinity isn't an integer. Since there is no integer $n$ such that $n=n+1$, you're right that the set is empty.