This is proposition 10.26 in Atiyah Macdonald I was trying to prove it. In the proof they are using $ \hat{A}$ is complete implies $\bigcap^{\infty}_{n=0}\hat{I^n}=(0) $
I am not getting how to prove this, I took $x \neq 0\in \bigcap^{\infty}_{n=0}\hat{I^n}$ and tried to construct cauchy sequence $(x+\hat{I^n})_n$ but I am not getting any contradiction.
can I get some hint to prove $\bigcap^{\infty}_{n=0}\hat{I^n}=(0) $