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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?

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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.

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