Homework Help Overview
The discussion revolves around identifying an example of a linear subset of a Hilbert space that is not closed. The original poster seeks clarification on the properties of such subsets, particularly in the context of infinite dimensional Hilbert spaces.
Discussion Character
- Exploratory, Conceptual clarification
Approaches and Questions Raised
- Participants discuss the nature of a specific subset defined by a finite combination of basis elements and question its closure properties. There is an exploration of sequences within this subset and their convergence behavior.
Discussion Status
The conversation includes attempts to clarify why certain subsets are not closed, with participants expressing confusion about convergence and limits within the context of Hilbert spaces. There is an ongoing exploration of the implications of completeness in these spaces.
Contextual Notes
Participants note that the discussion is focused on infinite dimensional Hilbert spaces, suggesting that closure properties differ from those in finite dimensional spaces.