The discussion revolves around proving the existence of unique positive integers m and n for a given real number x, specifically that m satisfies m ≤ x < m + 1 and n satisfies n < x ≤ n + 1. The context is mathematical reasoning related to properties of real numbers and integers.
Participants are engaging in a dialogue about the proof's requirements and structure. Some guidance has been offered regarding the use of supremum in defining m and n, but there is no explicit consensus on the proof's details or completeness.
There is an emphasis on adhering to forum rules regarding homework help, indicating that participants are encouraged to assist in understanding rather than providing direct answers. The original poster's repeated request suggests a need for clarification on the proof process.
Suppose there are 2 sets X and Y, X={k belongs to Z : k<x}, Y={k belongs to Z : k<=x}, which means X and Y are not set zero and there should be a sup. Now you only need to let m=supX and n=supY then try to prove m belongs to X and n belongs to Y. Thats all.YourLooks said:
