Hi, I posted a little while ago asking about questions from the bookNumbers and Symmetryby Bernard Johnston (Circular Numbers). I am still having a little trouble with the questions concerning these "circular numbers":

1.What is $\displaystyle \mathbb{Z}_{\infty}$?

I am unclear on how to answer this because I am unclear on what exactly is meant by $\displaystyle \mathbb{Z}_n$. The book prefers a rather indirect approach to the topic. Previously I guessed that it is equal simply to $\displaystyle \mathbb{Z}$ (the regular integers), or maybe just the nonnegative integers.

2.Describe all units and zero divisors in $\displaystyle \mathbb{Z}$.

I find it difficult to answer this question seeing as I can't even answer the first one. If $\displaystyle \mathbb{Z}_{\infty}$ is indeed equal to the set of nonnegative integers, then I think all the units in it would be such members as multiply to $\displaystyle \infty - 1$, which I assume is just $\displaystyle \infty$ and therefore there are no such members. Likewise, zero divisors would be such members as multiply to zero, which is the same as $\displaystyle \infty$ in $\displaystyle \mathbb{Z}_{\infty}$ - and so there are neither any zero divisors. I really have no idea about this question, however, and these are just my wildest guesses.

I really appreciate any insights. I am a total beginner at algebra.