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?
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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.
answered Nov 24, 2014 at 22:43
$\begingroup$
$\endgroup$
3
This is an empty set which is usually denoted by {}. In this case, the integer n is equal to itself while incremented by 1 which is mathematically impossible. Thus, this is an empty set.
EX: n = 2, then n = n + 1, 2 = 2 + 1. This is impossible.
-
1$\begingroup$ Why those downvotes ? $\endgroup$– user16034Sep 3 at 18:35
-
2$\begingroup$ This is an ancient question that already had a better answer. $\endgroup$– KaiSep 4 at 4:23
-
$\begingroup$ (downvoters please comment what in particular makes a post not useful.) $\endgroup$ Sep 4 at 5:25