- #1

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- Homework Statement
- I've got a piecewise function, and wanted to demonstrate its continuity using sequences

- Relevant Equations
- ##f(x)=\begin{cases}{\left|{x}\right|}&\text{if}&x\in\mathbb{Q}\\0&\text{if}&x\not\in\mathbb{Q}\end{cases}##

I've been given the proof, but don't understand; to calculate the limit of ##f## when ##x## tends to zero it's enough to see that if ##\{x_n\}_{n=1}^\infty## is a sequence that tends to ##0##, then $$f(x_n)=\begin{cases}{\left|{x_n}\right|}&\text{if}&x\in\mathbb{Q}\\0&\text{if}&x_n\not\in\mathbb{Q}\end{cases}$$ clearly tends to ##0##. Hence, ##\lim_{x\to 0}f(x)=0##

Question: why ##f(x_n)## tends clearly to zero?. I know I've already answered it on this post, but I don't understand.

PS: If the place I've published is the wrong one, please move it.

Question: why ##f(x_n)## tends clearly to zero?. I know I've already answered it on this post, but I don't understand.

PS: If the place I've published is the wrong one, please move it.