Rudin's proof that rationals have no GLB (or LUB)
119180
How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
102284
$GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$
67383
Prove that $G'$ is not planar.
234
No continuous function switches $\mathbb{Q}$ and the irrationals
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
49621
Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$"
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
38221
What is wrong with this proof there is no $\omega$-th worldly cardinal
78263
Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
17525
Why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty?
30753
Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)