Homework Help Overview
The discussion revolves around the algebraic structure of R/Z under addition, specifically questioning whether it contains an infinite number of elements of order 4. The original poster presents an initial claim regarding the existence of such elements based on cosets formed by primes.
Discussion Character
- Exploratory, Assumption checking
Approaches and Questions Raised
- The original poster attempts to justify their claim by referencing cosets of the form p/4 + Z for primes p greater than 2. Another participant questions the validity of this approach by noting that each prime greater than 2 can only yield two distinct cosets modulo 4.
Discussion Status
The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been provided regarding the limitations of the original poster's reasoning, but no consensus has been reached on the overall question.
Contextual Notes
Participants are examining the implications of modular arithmetic and the properties of primes in relation to the order of elements in the group R/Z.
