Show that if $r \in \mathbb{Q}$ is such that $\phi(r)=r$, than $\phi$ is the classic affine function.
120935
Why is every continuous function on the reals determined by its value on rationals?
97009
Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
84021
How can we show that $\varphi(a) \neq a +1$ for every $a \in A$?
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
137982
Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$
125894
Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
152347
Proof that a certain entire function is a polynomial
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
145865
Showing a set is an affine variety
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?