- #31
johnqwertyful
- 396
- 14
NATURE.M said:
No more than you need to justify n+1>n.
Explaining Why 1.1 and 0.95 Are Not Least Upper Bounds for Set A
- Thread starter NATURE.M
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- Bounds
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Homework Help Overview
The discussion revolves around the identification of the least upper bound (lub) for a set A, which consists of numbers of the form n/(n+1) where n is a positive integer. Participants are tasked with explaining why the numbers 1.1 and 0.95 cannot be considered the lub of this set.
Discussion Character
- Conceptual clarification, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Some participants explore the properties of the least upper bound axiom and question the validity of the original poster's reasoning regarding 1.1 and 0.95. There are discussions about providing specific examples to demonstrate that these numbers do not satisfy the conditions for being the lub. Others suggest that the original poster's proof may be overly complex and could benefit from a more straightforward approach.
Discussion Status
The conversation is ongoing, with participants offering guidance on how to structure proofs and clarify concepts related to upper bounds. There is recognition of the need to demonstrate specific examples that contradict the claim of 1.1 and 0.95 being the lub. Multiple interpretations of the problem are being explored, and some participants express uncertainty about the formalism of proofs.
Contextual Notes
Participants note the importance of adhering to forum rules regarding homework help, emphasizing that the original poster should arrive at their own conclusions rather than receiving direct solutions. There is also mention of the limit of the function as n approaches infinity, which may be relevant to the discussion of the lub.
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