query: Prove that this vector space is not finite dimensional.
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: 6547
negative_passages.text: Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
negative_passages.docid: 7828
negative_passages.text: Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
negative_passages.docid: 12189
negative_passages.text: Prove norm doesn't come from inner product.
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 151637
negative_passages.text: How do we prove that this set is not manifold?
negative_passages.docid: 144151
negative_passages.text: An orthonormal set cannot be a basis in an infinite dimension vector space?
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 11259
negative_passages.text: Prove $R\times S$ is not an integral domain
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 60692
negative_passages.text: Is this map to a finite dimensional topological vector space an open map?
negative_passages.docid: 99300
negative_passages.text: Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
negative_passages.docid: 41520
negative_passages.text: Prove that $L(V,W)$ forms a vector space
negative_passages.docid: 38033
negative_passages.text: A surjective linear map into a finite dimensional space is open
negative_passages.docid: 137873
negative_passages.text: Problems that involves two facts in the definition of vector spaces