What does the set $2\mathbb{Z}$ mean?

Question

What does the set $2\mathbb{Z}$ mean?

I know $\mathbb{Z}$ is the set that contains all the integer numbers, but what does $2\mathbb{Z}$ mean?

Answer 1

$2\mathbb{Z}$ is the set of even numbers.

That is: $2\mathbb{Z}=\{2z\ |\ z\in\mathbb{Z}\}$

Answer 2

$$\begin{align} \Bbb{Z} &= \{ \cdots, -3,-2,-1,0,1,2,3,\cdots\} \\ 2\Bbb{Z} &= \{ \cdots, (-3\cdot2),(-2\cdot2),(-1\cdot2),(0\cdot2),(1\cdot2),(2\cdot2),(3\cdot2),\cdots\} \\ &= \{ \cdots,-6,-4,-2,0,2,4,6,\cdots\} \end{align}$$