Homework Help Overview
The discussion revolves around proving the convergence of a sequence (f(x_n)) in the reals, given that (x_n) converges to a point x in a metric space (E,d). The problem touches on the concept of continuity in metric spaces.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the implications of continuity for the function f and its effect on the convergence of the sequence (f(x_n)). There is a discussion about the necessity of continuity for the proof and examples are provided to illustrate potential pitfalls when f is not continuous.
Discussion Status
The discussion is ongoing, with participants questioning the assumptions regarding the continuity of the function f. Some have pointed out that without continuity, the original poster's assertion may not hold true. There is an exploration of different scenarios and examples to clarify these points.
Contextual Notes
It is noted that the problem does not specify whether the function f is continuous, which is central to the discussion. This lack of information is causing uncertainty in the participants' reasoning.