# Thread: Annihilator

1. ## Annihilator

I am having problems showing $\displaystyle X\subseteq ann(ann(X))$. I don't understand how I would start this problem and don't understand what the annihilator of an annihilator would be.

Thanks for the help!

2. Originally Posted by Kiwili49
I am having problems showing $\displaystyle X\subseteq ann(ann(X))$. I don't understand how I would start this problem and don't understand what the annihilator of an annihilator would be.

Thanks for the help!

Let $\displaystyle x\in X\Longrightarrow nx=0\,\,\,\forall\,n\in Ann(X)\Longrightarrow\,x$ annihilates every $\displaystyle n\in Ann(X)\Longrightarrow\,x\in\,Ann(Ann(X))$

Tonio

3. That is really helpful! I am still lost, though, on the last implication.

4. Originally Posted by Kiwili49
That is really helpful! I am still lost, though, on the last implication.

I can't make it clearer than that. I think you must check your definitions and make sure you understand them well: the proof is exactly in my post!

Tonio