Question

What are the dimensions of R^2, R^3, R^n? (Linear Algebra)

Answer 1

2,3, and n
...I don't really have a fitting explanation

Answer 2

\(\mathbb{R^x}\) for \(x\in\mathbb Z,x\geq0\) means, in terms of construction, that I have \(x\) many orthogonal vectors forming the linearly independent bases of the space \(\mathbb{R^x}\). The \(\mathbb R\) part just means that this space is all the reals.

Answer 3

Also, it feels kind of funny defining \(\mathbb{R^x}\) with a relationship between \(x,\mathbb Z\), but while it may not be rigorous, this is how I heuristically understand it.

Answer 4

I just had to look up 'heuristic', lol.
You sure have the gift of gab br!
good explanation though