What does this set mean: $ \{ g \mid g : \{0,1\} \rightarrow \mathbb{N} \} $

Question

I have an excercise and there is the set $ \{ g\mid g : \{0,1\} \rightarrow \mathbb{N} \} $. Now I wanted to know, that this set mean? What's the content of it? I know normal sets very well but in my oppinion this has to be a set of functions and I have no idea how it would look like...

Thanks

Answer 1

It's the set the functions which have domain $\{0,1\}$ and image a subset of $\Bbb N$.

Answer 2

It means that the set consists of these functions $g$ such that $g : \{0,1\} \to \mathbb N$. This means that the function $g$ is defined over $\{0,1\}$ and thus its domain is the discrete points $0$ and $1$ and sends them to $\mathbb N$, thus its image is $\mathbb N$ or a subset of $\mathbb N$.

Answer 3

It's the set of functions that have a domain of $\{0,1\}$ and a codomain of $\Bbb N$. In other words, each $g$ is a function which sends $0$ and $1$ to a natural number and all such functions are in the set.

Answer 4

$g$ is a function which maps elements of the set $\{0,1\}$ to natural numbers. And this is the set of all such functions $g$

But, you could think of it as a set of ordered pairs $(x,y)$ with $x$ telling you where the function $g$ will map $0,$ and $y$ telling you where $g$ will map $1.$

Answer 5

I think of this set of functions as $\mathbb{N}^2$ because each function will give us a pair $(x_0,x_1)$ given by $(f(0),f(1))$ which will be natural numbers. In fact if I have some indexing set $I$ and some other set $X$ then I can define the Cartesian product of a set with itself as $\prod_{i \in I}X = \{g|g:I \rightarrow X\}$ which can be generalized with a little work.