How does axiom of foundation prevent infinite sequence of elements?

[Hill]

TL;DR

How does axiom of foundation prevent the infinite descending sequence of elements?

Axiom of foundation says, $\forall x (x\neq \emptyset \to \exists y(y\in x\wedge (y\cap x=\emptyset )))$.
The book says,
"As a consequence of the Axiom of Foundation, we see that there is no
infinite descending sequence x0 ∋ x1 ∋ x2 ∋ ···, since otherwise, the
set {x0,x1,x2,...} would contradict the Axiom of Foundation."

How does it contradict the Axiom of Foundation? If y=x0, it seems to obey the axiom.

 

[Hill]

Forget it. I misunderstood the statement.

 

[nuuskur]

For the sake of completeness, suppose there is such a sequence. As it says in #1, take $x=\{x_0,x_1,\ldots\}\neq\emptyset$. Then $x_{k+1} \in x\cap x_k$ for all $k$, contradicting the axiom.