Hi, I posted a little while ago asking about questions from the book Numbers and Symmetry by Bernard Johnston (Circular Numbers). I am still having a little trouble with the questions concerning these "circular numbers":
1. What is ?
I am unclear on how to answer this because I am unclear on what exactly is meant by . The book prefers a rather indirect approach to the topic. Previously I guessed that it is equal simply to (the regular integers), or maybe just the nonnegative integers.
2. Describe all units and zero divisors in .
I find it difficult to answer this question seeing as I can't even answer the first one. If is indeed equal to the set of nonnegative integers, then I think all the units in it would be such members as multiply to , which I assume is just and therefore there are no such members. Likewise, zero divisors would be such members as multiply to zero, which is the same as in - 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.