My teacher mentioned this was a very important thing to know in calculus, he didn't explain too much about it but tried to emphasize how important is it.
If $$P=\{a,x,...,x_{k-1},x_{k},...,x_{n}=b\} , P^*=\{a,x,...,x_{k-1},x^*_{k},x_{k},...,x_{n}=b\}$$
Then...