Real numbers as a $\mathbb{Q}$-linear space
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
26256
Characterizing Dense Subgroups of the Reals
120522
Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
86362
Cyclic vectors in a real vector space
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
36325
Embedding ordinals in $\mathbb{Q}$
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
22391
Is the set of all pairs of real numbers uncountable?
152503
Rational numbers as vectors in infinite dimensional space with the basis $( \log 2,\log 3, \log 5, \log 7, \dots, \log p, \dots) $
106960
Proof to sequences in real analysis
8255
Real polynomials from repunits to repunits ( Putnam 2007 A4)
100759
Extending exponentiation to reals
5893
On the commutative property of multiplication (domain of integers, possibly reals)
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
70543
Does an uncountable discrete subspace of the reals exist?