query: Dimension of R over Q without cardinality argument.
positive_passages.docid: 17748
positive_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 89167
negative_passages.text: Cardinality of equivalence relations in $\mathbb{N}$
negative_passages.docid: 41347
negative_passages.text: The dimension of the intersection of two vector subspaces
negative_passages.docid: 34177
negative_passages.text: Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
negative_passages.docid: 109764
negative_passages.text: Find the cardinality of the quotient of $\mathbb R$ in respect to R
negative_passages.docid: 33188
negative_passages.text: Dimension of null space of a given problem
negative_passages.docid: 58490
negative_passages.text: Polynomials, finite fields and cardinality/dimension considerations
negative_passages.docid: 45216
negative_passages.text: Cardinality of $[0,1]$
negative_passages.docid: 110957
negative_passages.text: No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
negative_passages.docid: 31318
negative_passages.text: Cardinality of cartesian square
negative_passages.docid: 81471
negative_passages.text: Finite dimensional spaces
negative_passages.docid: 150605
negative_passages.text: Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
negative_passages.docid: 132386
negative_passages.text: Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
negative_passages.docid: 70543
negative_passages.text: Does an uncountable discrete subspace of the reals exist?
negative_passages.docid: 113606
negative_passages.text: Dimensionless quantities
negative_passages.docid: 94363
negative_passages.text: Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
negative_passages.docid: 3810
negative_passages.text: When is a function a dimension?