The discussion focuses on proving the continuity of the function defined as $$f(x)=\begin{cases}{\left |{x}\right |}&\text{if}& x \in \mathbb{Q}\\ 0 & \text{if}& x \not \in \mathbb{Q}\end{cases}$$ at the point zero. Participants emphasize that to show $$\lim_{x\to 0} f(x) = 0$$, one must demonstrate that for any sequence $$\{x_n\}$$ converging to zero, $$f(x_n)$$ also converges to zero. The proof requires using the formal definition of limits and continuity, specifically the epsilon-delta criterion, to establish that $$|f(x_n) - f(0)| < \epsilon$$ for sufficiently large $$n$$.
PREREQUISITESStudents of mathematics, particularly those studying real analysis, educators teaching calculus concepts, and anyone interested in understanding the formal proofs of continuity and limits.
Furthermore, it's the real thingFactChecker said:
Definitively, compañero.PeroK said:
Yes.WWGD said:
This... Was as simple as @PeroK knew; as hard as I turned it.Mark44 said:
Are the last two words Basque? I definitely don't recognize them as Spanish.mcastillo356 said:
Just basqueing in the glory of Spanish regional languages.Mark44 said: