Can we represent $\mathbb{R}$ to $\mathbb{C}$, such that: $\forall c \in \mathbb{C}: \exists x \in \mathbb{R}: f(x)=c$?
58636
Do the real numbers and the complex numbers have the same cardinality?
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
135772
how to show image of a non constant entire function is dense in $\mathbb{C}$?
155275
If two real matrices are conjugated over $\mathbb{C}$, are they then also conjugated over $\mathbb{R}$?
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
57581
Let $E$ be measurable and define $f:E\rightarrow\mathbb{R}$ such that $\{x\in E : f(x)>c\}$ is measurable for all $c\in\mathbb{Q}$, is $f$ measurable?
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
12213
Similarity of real matrices over $\mathbb{C}$
61640
Prove c exists for f:[0,1] -> R
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
17748
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?