The dimension of a vector space is the number of elements in the basis for that vector space.
If we look at $\mathbb R^n$, then we say that the dimension of $\mathbb R^n$ is $n$. So every element in $\mathbb R^n$ can be expressed as a linear combination of these $n$ elements in the basis.
We further say that the elements of $\mathbb R^n$ are $n$-tuples.
I am slightly confused as to what is the relation between the $n$ in the dimension of $\mathbb R^n$ and the $n$ in the $n$-tuple.
The $n$ dimension gaurantees that the elements of $\mathbb R^n$ will be $n$-tuples, right. However if we have $n$-tuples as elements of some arbitrary vector space then we cannot say that the dimension of that vector space is $n$.
Am i correct in this regard.