Epsilondelta

What is the inverse limit of $\{(1+p\mathbb Z_p)/(1+p^n\mathbb Z_p\}$ ??

Hello. Someone there who can help me (an algebra question)

:(

Let f be irreducible in F_p[X] for a prime p. How to show that f divides X^(p^n)-X if and only if deg(f) divides n?

okay

i am new here. can i ask questions here?

hello

Now i have to understand B=>A (A is the statement on the left hand side, and B is the statement on the right hand side of task 1) )

Okay, i understood the implication A=>B

So, for task 1). If we suppose the left hand side: X_n -> 0. Can i conclude, that:

i am just new to probability theory

and i actually don't want to disturb you

No, I am not doing fun of you

Hello

Okay, i got it know. Last question:Why are you only considering $X=0$ and not also $X=1$? If all $X_n=1$ or $1$, then X could be 1 too.

But what about the $p_n$?I thought this notation does mean: $P(X_n=0)=P(X_n^{-1}(0))=p_n$ I thought thats just a property on a certain set and we don't know anything about the other values. I am reading it like: "The measure of the fiber under all $X_n$ of zero is exactly $p_n$"

Thats the thing I don't understand. I am sorry for this probably stupid question. But why $X_n$ does only take two values?

Thanks for the answer! I am trying to understand your proof of 1). I dont understand the sentence "But since $X_n$ is equal to one or zero..." and the steps after this. Can you explain it to me in more detail please?