query: Given that 1D space $\mathbb{R}$ and 3D space $\mathbb{R}^3$ are in bijection, why do we describe our physical world as 3D?
positive_passages.docid: 37327
positive_passages.text: Is 3+1 spacetime as privileged as is claimed?
negative_passages.docid: 137781
negative_passages.text: Can anybody explain about real linear space and complex linear space?
negative_passages.docid: 25854
negative_passages.text: $\mathbb{R}^3$ \ $\mathbb{Q}^3$ is union of disjoint lines. The lines are not in an axis diretion.
negative_passages.docid: 78108
negative_passages.text: Do these define metrics on $\mathbb{R}$?
negative_passages.docid: 128266
negative_passages.text: Dual Spaces and Natural maps
negative_passages.docid: 48598
negative_passages.text: What's the difference between $\mathbb{R}^2$ and the complex plane?
negative_passages.docid: 22150
negative_passages.text: The only 1-manifolds are $\mathbb R$ and $S^1$
negative_passages.docid: 23837
negative_passages.text: Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
negative_passages.docid: 54333
negative_passages.text: In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?
negative_passages.docid: 97801
negative_passages.text: If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
negative_passages.docid: 81471
negative_passages.text: Finite dimensional spaces
negative_passages.docid: 64920
negative_passages.text: Boundary Question in $\mathbb{R}^{2}$ (Manifolds)
negative_passages.docid: 27757
negative_passages.text: $\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 95086
negative_passages.text: Homeomorphism is bijective
negative_passages.docid: 86234
negative_passages.text: Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field
negative_passages.docid: 114142
negative_passages.text: How to show that $\mathbb{R}^3$ is the direct sum of $W_1={\rm span}\{(1,1,1)\}$ and $W_2={\rm span}\{(1,0,0),(1,1,0)\}$?