The cardinality of $\{f\subseteq\mathbb R^2\mid f\colon\mathbb{R\to R}\text{ is a function}\}$ is strictly greater than the cardinality of $\mathbb R$
102972
Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
41557
Most general $A \subseteq \mathbb R$ to define derivative of $f: A \to \mathbb R$?
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
146436
Cardinality of the set of bijective functions on $\mathbb{N}$?
108957
Cardinality of a totally ordered union
68230
The cardinality of a countable union of sets with less than continuum cardinality
63146
Proof of properties of injective and surjective functions.
82628
Cardinality of a set of closed intervals
127233
Cardinality of order types in $\mathbb{N}$
35043
Cardinality of a set A is strictly less than the cardinality of the power set of A
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
81509
The cardinality of a countable union of countable sets, without the axiom of choice
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
97697
Countable union of sets of cardinality $c$ has cardinality $c$