1
$\begingroup$

As far as I have understood the cartesian product, $\mathbb{R}^2 = \{(x,y) \ \vert \ x \in \mathbb{R} \ \land \ y \in \mathbb{R} \}$, contains ordered pairs, represented as tuples.
But think I have also seen $\vec{v} \in \mathbb{R}^2$.

Firstly, is that correct?
Secondly, does that mean that the elements of $\mathbb{R}^2$ can be represented as vectors as well?
In general, what is the relationship between cartesian vectors and tuples?

$\endgroup$
0
$\begingroup$

Tuples (in general points in $R^n$) are points in space. Vectors have a length and direction. A one to one correspondence between vectors and points in space can be made by fixing the tail of a vector to the origin and the head of the vector at that point in space.

Note that vectors themselves are free floating - allowing addition, etc.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy