Question

Where is the flaw in this proof by induction?

score 120 · Answer 1 · 2026-03-28 22:26:38

120

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Where is the flaw in this proof by induction?

Published on 28 Mar 2026 - 22:26

score 29 · Answer 2 · 2026-03-27 02:37:42

29

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$(m, m') \in \mathit R^{n}$ only when sequence $c_0, ..., c_n$ $\mathit M$ with $m = c_0, (c_1, c_{i+1}) \in \mathit R$ and $c_n = m'$ exists

Published on 27 Mar 2026 - 2:37

score 411 · Answer 3 · 2026-03-31 15:24:56

411

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Let R be a relation on a set X. Then R is transitive if and only if, for any finite sequence x0, x1,..., xn of elements...

Published on 31 Mar 2026 - 15:24

score 127 · Answer 4 · 2026-03-28 22:30:56

127

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Sum involving Binomial numbers and Fibonacci numbers

Published on 28 Mar 2026 - 22:30

score 67 · Answer 5 · 2020-03-15 22:52:16

67

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Given $ \frac {p} {q} $, can you achieve to paint the point C such that $\frac{AC}{CB} = \frac {p} {q}$ with permitted operations

Published on 15 Mar 2020 - 22:52

score 165 · Answer 6 · 2020-03-16 15:58:23

The result of the bi-conditional $\leftrightarrow$ is true when n is odd and m is odd, and when n is even and m is even. Proof by induction

score 365 · Answer 7 · 2020-03-16 19:39:23

365

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On Mathematical Induction

Published on 16 Mar 2020 - 19:39

score 31 · Answer 8 · 2026-04-02 19:54:19

31

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Find minimum $x$ such that for all $y\geq x$, a combination of cents exists that adds upto $y$. ($p_1$ to $p_n$ denominations of cents available).

Published on 02 Apr 2026 - 19:54

score 263 · Answer 9 · 2020-03-17 13:28:04

263

Views

If $m_n + n$ is true, then prove that $m_{n+1} + n + 1$ is true. Algebraic breakdown help

Published on 17 Mar 2020 - 13:28

score 790 · Answer 10 · 2020-03-17 18:21:34

790

Views

Generalized Union and Intersection by Induction

Published on 17 Mar 2020 - 18:21

score 42 · Answer 11 · 2026-03-31 16:06:47

42

Views

If $(Y,\mathcal{F})$ is a martingale, show that $\mathbb{E} (Y_n)=\mathbb{E}(Y_0)$ for all n.

Published on 31 Mar 2026 - 16:06

score 52 · Answer 12 · 2020-03-18 18:52:15

52

Views

Given a series $b_0,b_1,...$, where $b_0=1,b_1 = 2,b_2 = 3$ and $b_n=b_{n-3}+b_{n-2}+b_{n-1}$, show $b_n \leq 3^n$ for $n>2$.

Published on 18 Mar 2020 - 18:52

score 853 · Answer 13 · 2026-03-26 11:18:18

853

Views

Inductive proof showing a tiling of trominoes on a $2i \times 3j$ board with no squares missing.

Published on 26 Mar 2026 - 11:18

score 118 · Answer 14 · 2026-04-07 23:45:38

118

Views

Derivative of exponential with function argument

Published on 07 Apr 2026 - 23:45

score 167 · Answer 15 · 2026-03-25 11:10:10

167

Views

Prove $B_n\le n! $ for Bell numbers

Published on 25 Mar 2026 - 11:10

List Question

Where is the flaw in this proof by induction?

$(m, m') \in \mathit R^{n}$ only when sequence $c_0, ..., c_n$ $\mathit M$ with $m = c_0, (c_1, c_{i+1}) \in \mathit R$ and $c_n = m'$ exists

Let R be a relation on a set X. Then R is transitive if and only if, for any finite sequence x0, x1,..., xn of elements...

Sum involving Binomial numbers and Fibonacci numbers

Given $ \frac {p} {q} $, can you achieve to paint the point C such that $\frac{AC}{CB} = \frac {p} {q}$ with permitted operations

The result of the bi-conditional $\leftrightarrow$ is true when n is odd and m is odd, and when n is even and m is even. Proof by induction

On Mathematical Induction

Find minimum $x$ such that for all $y\geq x$, a combination of cents exists that adds upto $y$. ($p_1$ to $p_n$ denominations of cents available).

If $m_n + n$ is true, then prove that $m_{n+1} + n + 1$ is true. Algebraic breakdown help

Generalized Union and Intersection by Induction

If $(Y,\mathcal{F})$ is a martingale, show that $\mathbb{E} (Y_n)=\mathbb{E}(Y_0)$ for all n.

Given a series $b_0,b_1,...$, where $b_0=1,b_1 = 2,b_2 = 3$ and $b_n=b_{n-3}+b_{n-2}+b_{n-1}$, show $b_n \leq 3^n$ for $n>2$.

Inductive proof showing a tiling of trominoes on a $2i \times 3j$ board with no squares missing.

Derivative of exponential with function argument

Prove $B_n\le n! $ for Bell numbers

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