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## Main Question or Discussion Point

**"Open" set challenging question and mind-blogging concept!Welcome.**

This statement is correct.

[tex]\left\{\left[1,3-\frac{1}{n}\right)\right\}_{n\in\mathbb Z} \text {is an "OPEN" cover of}\left[1,3\right)[/tex]

BUT WHY OPEN?

There are 3 options.

1.All [itex]\left[1,3-\frac{1}{n}\right)[/itex] is the open set in [itex]\mathbb Z[/itex];

or

2.All [itex]\left[1,3-\frac{1}{n}\right)[/itex] is the open set in [itex]\left[1,3\right)[/itex].

or

3.All [itex]\left[1,3-\frac{1}{n}\right)[/itex] is the open set in [itex]\mathbb R^{1}[/itex]

Which one?

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