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Topology

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Moderate

Dense Subsets Of Real Numbers

TOPO-QGW4EB

Consider the real numbers $\mathbb{R}$ equipped with the usual topology. Which of the following subsets are dense?

Select ALL that apply.

A

$\mathbb{Z}$

B

$\mathbb{Q}$

C

$\{x\in\mathbb{R} : x\notin\mathbb{Q}\}$

D

$\{x\in\mathbb{R} : f(x)=0$ for some polynomial $f$ with integer coefficients $\}$

E

$\mathbb{Q} - \{0\}$