Recently I've found in a problem the term "countable dense sequence" in one interval and it really confused me. The point is: I know what a countable dense subset of an interval is – it is one countable subset of the interal, such that its closure is the whole interval.

In other words, any point on the interval is the limit of a sequence of points of the set, that in the particular case, happens to be countable.

Now, countable dense sequence is a term I never heard and I didn't find any definition whatsoever.

What it means to speak of "a countable dense sequence $\{r_n\}$ on the interal $[0,1]$"?

## Best Answer

What is meant is that the set $$\{r_n,n\in\mathbb{N}\}$$ is countable and dense in $[0,1]$.