Question

Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

score 1.4k · Answer 1 · 2026-03-25 08:13:41

1.4k

Views

Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

Published on 25 Mar 2026 - 8:13

score 195 · Answer 2 · 2026-03-25 09:50:00

195

Views

Prove Cardinality of set of Bijections in $\mathbb{N} \to \mathbb{N}$ is $\mathfrak {c}$

Published on 25 Mar 2026 - 9:50

score 2.2k · Answer 3 · 2026-03-23 18:18:56

2.2k

Views

Is the set of terms of a sequence countable?

Published on 23 Mar 2026 - 18:18

score 89 · Answer 4 · 2026-03-23 22:23:35

89

Views

Bijection from set of bounded real-valued functions B(X) to $\mathbb R^{n}$?

Published on 23 Mar 2026 - 22:23

score 60 · Answer 5 · 2026-03-24 15:24:38

60

Views

Explicit example of saturated (complete) set

Published on 24 Mar 2026 - 15:24

score 29 · Answer 6 · 2026-03-23 23:51:48

29

Views

Query on countability of sets and its subset 1

Published on 23 Mar 2026 - 23:51

score 581 · Answer 7 · 2026-04-10 15:14:30

581

Views

What is this set notation called?

Published on 10 Apr 2026 - 15:14

score 55 · Answer 8 · 2026-03-24 10:55:37

55

Views

Want an alternate solution to this set theory Q

Published on 24 Mar 2026 - 10:55

score 51 · Answer 9 · 2026-03-24 03:58:07

51

Views

Proof A=C or B=C

Published on 24 Mar 2026 - 3:58

score 205 · Answer 10 · 2026-03-24 23:51:34

205

Views

Prove that $f(x+y)=f(x)+f(y)$, and $f(x\cdot y) = f(x)\cdot f(y)$ implies $f:\mathbb{R} \to \mathbb{R}'$ is a bijective mapping that preserves order.

Published on 24 Mar 2026 - 23:51

score 439 · Answer 11 · 2026-03-24 22:01:52

439

Views

How can a bijection from $\mathbb R^n \to \mathbb R$ exist when a non square matrix is not invertible?

Published on 24 Mar 2026 - 22:01

score 49 · Answer 12 · 2026-03-25 09:48:50

49

Views

Set of Equivalence relations over $\mathbb{R}$

Published on 25 Mar 2026 - 9:48

score 65 · Answer 13 · 2026-03-26 09:18:05

65

Views

Proof verification: $f(S\cup T) = f(S) \cup f(T)$, where $S$ and $T$ are subsets of the set $A$ and $f$ is a function from $A$ to $B$.

Published on 26 Mar 2026 - 9:18

score 91 · Answer 14 · 2026-03-26 17:29:17

91

Views

General name for a multidimensional function that maps each coordinate independently

Published on 26 Mar 2026 - 17:29

score 35 · Answer 15 · 2026-03-24 05:42:37

35

Views

Finding the inverse of a function $F:\mathbb{P}_2 \rightarrow \mathbb{R}^2$

Published on 24 Mar 2026 - 5:42

List Question

Show that for a finite set $A$ of cardinality $n$, the cardinality of $P(A)$ is $2^n$.

Prove Cardinality of set of Bijections in $\mathbb{N} \to \mathbb{N}$ is $\mathfrak {c}$

Is the set of terms of a sequence countable?

Bijection from set of bounded real-valued functions B(X) to $\mathbb R^{n}$?

Explicit example of saturated (complete) set

Query on countability of sets and its subset 1

What is this set notation called?

Want an alternate solution to this set theory Q

Proof A=C or B=C

Prove that $f(x+y)=f(x)+f(y)$, and $f(x\cdot y) = f(x)\cdot f(y)$ implies $f:\mathbb{R} \to \mathbb{R}'$ is a bijective mapping that preserves order.

How can a bijection from $\mathbb R^n \to \mathbb R$ exist when a non square matrix is not invertible?

Set of Equivalence relations over $\mathbb{R}$

Proof verification: $f(S\cup T) = f(S) \cup f(T)$, where $S$ and $T$ are subsets of the set $A$ and $f$ is a function from $A$ to $B$.

General name for a multidimensional function that maps each coordinate independently

Finding the inverse of a function $F:\mathbb{P}_2 \rightarrow \mathbb{R}^2$

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