# Why is the physical space equivalent to $\mathbb{R}^3$ [closed]

I am trying to understand what would be the logical reasons behind our assumption that our physical space is equivalent to $\mathbb{R}^3$ or 'physical straight line' is equivalent to $\mathbb{R}$.

$\mathbb{R}$ is a basically an algebraically constructed set, which is nothing but the completion of $\mathbb{Q}$, the set of rationals. Now my question is what is the reason behind our approximation of the physical space by this abstract set. Why is this approximation assumed to be most suitable or good approximation ?

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## closed as off topic by DamienC, Chris Gerig, Qiaochu Yuan, Dan Petersen, Chris GodsilAug 30 '12 at 11:41

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Shouldn't you be asking a physicist? The reason for the goodness of the approximation is, ultimately, not mathematical. – Mariano Suárez-Alvarez Aug 30 '12 at 7:09
I believe that this is a bit off-topic, and actually not a real question. – DamienC Aug 30 '12 at 7:13
@Damien: I also thought people may find it off-topic, what do you mean by a real question ? – Pritam Majumder Aug 30 '12 at 7:21
Maybe I would add the word "locally"... and from a mathematical point of view, I would say that $\mathbb{R}$ is not only an algebraic construction (that would maybe be true for algebraic numbers), but you are strongly considering it's topology. – Michele Triestino Aug 30 '12 at 7:25
Maybe this has something to do with the fact that $\mathbb{R}$ is the unique complete ordered field up to isomorphism. – Qfwfq Aug 30 '12 at 12:09