Let $A$ be a set that is countable. Let there be a function mapping $A$ onto a set $B$. Is $B$ countable?
98151
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
70143
Mutually exclusive countable subsets of a countable set
11959
What's wrong with this argument that $[0,1]$ is countable?
97697
Countable union of sets of cardinality $c$ has cardinality $c$
44623
Closed set as a countable intersection of open sets
44974
Infinite set and countable subsets
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
118595
Proving that a set is countable by finding a bijection
7733
If A is infinite, does there have to exist a subset of A that is equivalent to A?
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
154474
Image of countable and uncountable sets
150346
If $f$ is an increasing function defined on $[a,b]$ . Then, $f$ has countable number of discontinuities
91237
Every infinite set contains a countable subset
63276
Is an arbitrary union of a chain of countable sets countable?
49592
Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
2269
Proof that the real numbers are countable: Help with why this is wrong
88201
Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.