If $f:\mathbb{R}\to\mathbb{R}$ then $|f(\mathbb{N})|\leq\aleph_0$
141298
Image of the set of natural numbers under any function is denumerable.
127488
If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
61640
Prove c exists for f:[0,1] -> R
56628
If $f: D(0,1)\to \mathbb C$ is holomorphic, then there is a sequence $\{z_n\}$ in $D(0,1)$ such that $|z_n| \to 1$ and $\{f(z_n)\}$ is bounded
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
118154
$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
98772
Continuity of a function in $\mathbb{R}$
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$