What does the notation $2\mathbb{Z}$ mean? I have an assignment that is asking to define a one-to-one correspondence between the sets $2\mathbb{Z}$ and $17\mathbb{Z}$... or in other words, define some bijective function on
$$f:2\mathbb{Z}\to 17\mathbb{Z}$$
Note: I know that $\mathbb{Z}$ is the set of integers.. I'm just wondering what the number in front means.

Addendum:
Given that I now know what these sets represent... is this a satisfactory answer for the question?

A one-to-one correspondence between $2\mathbb{Z}$ and $17\mathbb{Z}$ could be as follows:
\begin{align*}
  0&\mapsto 0\\
  2&\mapsto 17\\
  -2&\mapsto -17\\
  4&\mapsto 34\\
  -4&\mapsto -34\\
  6&\mapsto 51\\
  -6&\mapsto -51\\
\end{align*}
And so on...
In general, the function
\begin{equation*}
  f:2\mathbb{Z}\to 17\mathbb{Z}:2x\mapsto 17x,\forall x\in\mathbb{Z}
\end{equation*}
defines a one-to-one correspondence between the sets $2\mathbb{Z}$ and $17\mathbb{Z}$.
 A: $2\mathbb Z$ means the set $\{ 2\cdot n \mid n\in \mathbb Z\}$; that is, the set of even integers.
In general, $n\mathbb Z$ means the set of integer multiples of $n$.
Is your  question asking for  a bijection between $\{\ldots -6, -4, -2, 0, 2, 4, 6,\ldots\}$ and
 $\{\ldots -51, -34, -17, 0, 17, 34, 51,\ldots\}$?
A: $\;2\mathbb Z\;$ denotes the set of all integer multiplies of $\,2$: $$2\mathbb Z = \{2k\mid k\in \mathbb Z\}$$
The set $\;17\,\mathbb Z\;$ denotes the set of all integer multiplies of $\,17$: $$17\,\mathbb Z = \{17k\mid k \in \mathbb z\}$$
You'll encounter the notation frequently: In general, $$\;n\mathbb Z = \{nk\mid k \in \mathbb Z\}$$

EDIT to answer added question:
For your bijection: Yes, you've got the idea: let your bijection $f: 2 \mathbb Z \to 17 \mathbb Z\,$ be defined by $\,2k\mapsto 17k\,$ for each $\,k \in \mathbb Z,\,$ and yes, that includes $0 \mapsto 0$.
Edit: you're map that you just added will work, sort of, but you'll need to be clear that $n$ is a regular old integer (add tag following definition of function): $\forall n \in \mathbb{Z}$, otherwise n will refer to an element of $2\mathbb{Z}$. But then you are really mapping from $\mathbb Z \to 17\mathbb Z$. 
If you want $n \in 2\mathbb Z$ then use $$f: 2\mathbb{Z} \to 17\mathbb Z, \;\;f(n) = \dfrac 12 n \cdot 17, \;\forall n \in 2\mathbb{Z}.$$ That way you are mapping directly from an even number $n \in 2\mathbb Z \to f(n)\in 17\mathbb Z$
A: The set of even integers. Generally: $$n\Bbb Z=\{nk\mid k\in\Bbb Z\}$$
A: If $A$ is a subset of a vector space, the notation $\lambda A$ (where $\lambda$ is in the relevant field) generally means $\lambda A = \{ \lambda a \}_{a \in A}$.
A: I believe you can think of this as simply a special case of the notation $f(A)$, where $A$ is a subset of the domain of $f$, meaning the set of all images of elements of $A$. The $2$ or $17$ are essentially acting as symbols for the functions $2x$ and $17x$.
