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A sequence of continuous functions $(f_n\colon[a,b]\to\mathbf{R})_{n}$ is said to be point-wise bounded if for all $x\in[a,b]$ there is a $R_x>0$ such that $$|f_n(x)|\le R_x\quad\mbox{for all }n.$$

How can I visualize this definition? What kind of picture should I associate with this definition?

Thanks in advance.

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    I edited the tags of this post to include "intuition".2012-08-31

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