Prove the set of reals $\textbf{R}$ is not a finite-dimensional vector space over the set of rationals $\textbf{Q}$
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
84148
Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
139176
The real line is not homeomorphic to any non-trivial product space
69046
Proof of $\mathbb{Q}$ is not cyclic
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
57310
Prove $\mathbb{Z}$ is not a vector space over a field
82485
Show that the set of non zero rationals is not a cyclic group under multiplication.
28402
Number of bases of an n-dimensional vector space over q-element field.
42362
Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals