$\mathbb R^2$ as a plane

Question

What elements allow me to say that $\mathbb R^2$ can be seen simply as a plane (or not if that is the case)?

Yes, $\mathbb R^2$ is a vector space (not only with that characteristic) with multiple properties (such as these) and with properties I don't know. So, can I say: "$\mathbb R^2$ can be seen simply as a plane"?

I don't know if there are more appropriate tags – David Nov 26 '14 at 00:34 — David, Nov 26 '14 at 00:34
By definition, a plane is a 2-dimensional vector space – Andrea Mori Nov 26 '14 at 00:40 — Andrea Mori, Nov 26 '14 at 00:40
What do you want a "plane" to satisfy? – rschwieb Nov 26 '14 at 01:40 — rschwieb, Nov 26 '14 at 01:40

score 2 · Accepted Answer · answered Nov 26 '14 at 00:42

I'd say that $\mathbb R^2$ can be seen as simply a plane in much the same sense that you can be seen as simply an assemblage of atoms. Yes, it and you can be seen in those ways, and for some purposes it might be useful to do so, but it would ignore many important properties of $\mathbb R^2$ and of you.

$\mathbb R^2$ as a plane

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