Understanding an example in Ramsey Theory

I will just pick

$$1,2,3,4,5,6,7,8,9,10,11$$

The book says that

"You don't have to pick the numbers consecutively," Graham said" You can jump. You might pick the first one, then the nineteenth one, then the twenty-second one, then the thirty-eighth one-but they all have to be going up or going down"

Ramsey theory, says Graham, makes a generalization of this result: to guarantee either a rising or falling sequence of length $n + 1$, you need $n^2 + 1$ numbers; with $ n^2$ numbers, you may not get it.