query: True/False: $\mathbb{R}^2$ is a subspace of $\mathbb{R}^3$?
positive_passages.docid: 23740
positive_passages.text: Confused about the definition of subspace
negative_passages.docid: 145912
negative_passages.text: Whether the image is a subspace of a linear transformation
negative_passages.docid: 55026
negative_passages.text: $\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
negative_passages.docid: 98949
negative_passages.text: Subspaces and annihilators
negative_passages.docid: 86325
negative_passages.text: Is an increasing union of subspaces a subspace?
negative_passages.docid: 116273
negative_passages.text: Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
negative_passages.docid: 146243
negative_passages.text: Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 3543
negative_passages.text: Prove set is basis for $R^3$
negative_passages.docid: 110885
negative_passages.text: Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
negative_passages.docid: 67191
negative_passages.text: When is the union of a family of subspaces of a vector space also a subspace?
negative_passages.docid: 88051
negative_passages.text: $\mathbb R = X^2$ as a Cartesian product
negative_passages.docid: 124688
negative_passages.text: Question about a metric on $\mathbb{R}^2$
negative_passages.docid: 33944
negative_passages.text: Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 90525
negative_passages.text: The subspace of $\ell_2$