Question

Prove that cardinality of power set of X is equal to $2^n$, $\left | \mathcal{P}(X) \right | = 2^n$, using the principle of mathematical induction

score 2k · Answer 1 · 2026-04-14 03:52:59

Prove that cardinality of power set of X is equal to $2^n$, $\left | \mathcal{P}(X) \right | = 2^n$, using the principle of mathematical induction

score 263 · Answer 2 · 2026-04-16 16:51:25

263

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Inductive proof of $a_n = 32^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2a_{n-2}, a_1 = 1, a_2 = 8$

Published on 16 Apr 2026 - 16:51

score 286 · Answer 3 · 2026-04-11 11:42:52

286

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score 179 · Answer 4 · 2026-04-15 09:50:22

179

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Recursive function that doubles its input

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score 108 · Answer 5 · 2026-04-14 16:10:23

108

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score 85 · Answer 6 · 2026-04-15 07:36:28

85

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Induction proof involving divisibilty

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score 165 · Answer 7 · 2026-04-13 11:41:08

165

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Theorem in ACA that is unprovable in $Π^1_1$-CA$_0$?

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score 85 · Answer 8 · 2026-04-10 08:06:38

85

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score 76 · Answer 9 · 2026-04-13 23:10:34

76

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score 79 · Answer 10 · 2026-04-10 18:31:27

79

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Structural Induction - Bisimulation

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score 1000 · Answer 11 · 2026-04-17 21:21:37

1000

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Pascal triangle row totals by induction?

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score 777 · Answer 12 · 2026-04-15 10:33:30

777

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How can I prove that $\sinh (x) \leq x \cosh (x)$ for all $x \geq 0$?

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score 52 · Answer 13 · 2026-04-12 07:41:32

52

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Precise Statement of Strong Induction

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score 651 · Answer 14 · 2026-04-11 02:43:14

651

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Recursion problem

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score 39 · Answer 15 · 2026-04-11 22:27:12

39

Views

Proving Inequality Involving Powers of $2$ and $3$ Using Induction

Published on 11 Apr 2026 - 22:27

List Question

Prove that cardinality of power set of X is equal to $2^n$, $\left | \mathcal{P}(X) \right | = 2^n$, using the principle of mathematical induction

Inductive proof of $a_n = 32^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2a_{n-2}, a_1 = 1, a_2 = 8$

Proof by induction on Towers of Hanoi equation

Recursive function that doubles its input

Proof by induction, the difference of the same number is zero

Induction proof involving divisibilty

Theorem in ACA that is unprovable in $Π^1_1$-CA$_0$?

Induction for recursive function

Induction involving primes

Structural Induction - Bisimulation

Pascal triangle row totals by induction?

How can I prove that $\sinh (x) \leq x \cosh (x)$ for all $x \geq 0$?

Precise Statement of Strong Induction

Recursion problem

Proving Inequality Involving Powers of $2$ and $3$ Using Induction

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