Mathematical notation of set with $n+3$ members One of the math problems I have describes a set of numbers this way:

let there be a set A such that $A=\{{1,2,3,...,n+3}\}$.

I don't understand what the $n+3$ means and how the set actually looks like.
 A: The set is all positive integers between $1$ and $n + 3$, inclusive.
If $n = 4$, for example, the set is
$$
\{1, 2, 3, 4, 5, 6, 7\}.
$$
And if $n = 2$, then it's
$$
\{1,2,3,4,5\}.
$$
It may also be helpful to include a few more terms: $\{1, 2, 3, 4, \ldots, n, n+1, n+2, n+3\}$.
In general, $\{1, 2, 3, \ldots k\}$ is shorthand for the set of positive integers between $1$ and $k$, inclusive.
A: The $n$ is arbitrary and finite. Basically, choose an $n$ so
$$ A_n = \{ 1, 2, \ldots, n, n+1, n+2, n+3 \}.$$
For example, $A_4 = \{1, 2, \ldots, 5, 6, 7 \}.$
A: $n$ is just a natural number. So the set is of variable length. For example choosing $n=2$ yields $$A =\{1,2,3,4,5\}$$
A: For this to have a meaning, $n$ must be already defined.
For instance if $n=3$,
$$A=\{1,2,\ldots,n+3\}=\{1,2,3,4,5,6\}.$$
The "$n+3$" means that you are enumerating all integers from $1$ to $n+3$.
Another notation (to avoid the dots) would be
$$A=\{i\}_{1\leq i\leq n+3}.$$
A: Assuming for instance that $n$ must be a positive integer, this would be a way of forcing the set to have at least $4$ elements.
