Homework Help Overview
The discussion revolves around the concept of supremum and infimum in the context of set theory, specifically addressing the relationship between two sets A and B. The original poster seeks to demonstrate that if the supremum of set A is less than the supremum of set B, then there exists an element in set B that serves as an upper bound for set A.
Discussion Character
- Conceptual clarification, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants explore proof techniques, including proof by contradiction, and discuss the existence of an element in B that satisfies the upper bound condition. Questions arise regarding the implications of sup B not being an element of B and whether a contradiction can be established under such circumstances.
Discussion Status
The discussion is ongoing, with participants sharing different perspectives on the problem. Some suggest exploring specific examples to gain insight, while others express uncertainty about the reasoning presented. There is no explicit consensus yet, but various lines of reasoning are being examined.
Contextual Notes
Participants are considering the implications of the definitions of supremum and the conditions under which the elements of sets A and B are defined. The discussion acknowledges the challenge posed by the case where sup B is not included in B.