Question

there does not exist an injective function whose codomain is smaller than its domain

score 1.8k · Answer 1 · 2016-11-22 09:08:38

1.8k

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there does not exist an injective function whose codomain is smaller than its domain

Published on 22 Nov 2016 - 9:08

score 1k · Answer 2 · 2016-11-27 22:45:58

1k

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Prove that if six natural numbers are chosen at random, then the sum or difference of two of them is divisible by 9.

Published on 27 Nov 2016 - 22:45

score 145 · Answer 3 · 2016-11-28 12:48:42

145

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Properties of numbers picked from sets.

Published on 28 Nov 2016 - 12:48

score 122 · Answer 4 · 2016-12-03 14:35:42

122

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Generalised pigeonhole principle question

Published on 03 Dec 2016 - 14:35

score 350 · Answer 5 · 2016-12-06 10:34:08

350

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Pigeon hole principle solution explanation

Published on 06 Dec 2016 - 10:34

score 710 · Answer 6 · 2016-12-09 11:13:54

Prove that however one selects $55$ integers $1 ≤ x_1 < x_2 < x_3 < ... < x_{55} ≤ 100$, there will be some two that differ by 9, 10, 12 and 13.

score 733 · Answer 7 · 2016-12-11 17:54:01

733

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Discrete Math: Placing Points in A Random Way

Published on 11 Dec 2016 - 17:54

score 5.9k · Answer 8 · 2016-12-11 20:53:30

5.9k

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Pigeonhole Elementary School has 500 students. Show that at least two of them were born on the same day of the year.

Published on 11 Dec 2016 - 20:53

score 1.2k · Answer 9 · 2016-12-12 10:02:37

1.2k

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Not quite understanding parts of Pigeon Hole Principle Generalization

Published on 12 Dec 2016 - 10:02

score 143 · Answer 10 · 2016-12-26 08:43:50

143

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Prove at least two numbers $(a,b)$ exist such that $a|b$ or $b|a$.

Published on 26 Dec 2016 - 8:43

score 73 · Answer 11 · 2016-12-29 18:21:46

73

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A Question in Pigeonhole Principle

Published on 29 Dec 2016 - 18:21

score 6.1k · Answer 12 · 2016-12-30 23:44:24

Induction to prove that a set of $n+1$ integers between $1$ and $2n$ has at least one number which divides another number in the set

score 79 · Answer 13 · 2026-03-26 01:10:26

79

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Is $\sum_{p} \frac{1}{2^p}$ irrational?

Published on 26 Mar 2026 - 1:10

score 1.3k · Answer 14 · 2017-01-07 15:36:28

1.3k

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Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$

Published on 07 Jan 2017 - 15:36

score 633 · Answer 15 · 2017-01-10 18:30:10

633

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Prove that there exists at least one subset of the set $A=\{a_1,a_2,a_3,\dots,a_n\}$ such that the sum of its members is divisible by n.

Published on 10 Jan 2017 - 18:30

List Question

there does not exist an injective function whose codomain is smaller than its domain

Prove that if six natural numbers are chosen at random, then the sum or difference of two of them is divisible by 9.

Properties of numbers picked from sets.

Generalised pigeonhole principle question

Pigeon hole principle solution explanation

Prove that however one selects $55$ integers $1 ≤ x_1 < x_2 < x_3 < ... < x_{55} ≤ 100$, there will be some two that differ by 9, 10, 12 and 13.

Discrete Math: Placing Points in A Random Way

Pigeonhole Elementary School has 500 students. Show that at least two of them were born on the same day of the year.

Not quite understanding parts of Pigeon Hole Principle Generalization

Prove at least two numbers $(a,b)$ exist such that $a|b$ or $b|a$.

A Question in Pigeonhole Principle

Induction to prove that a set of $n+1$ integers between $1$ and $2n$ has at least one number which divides another number in the set

Is $\sum_{p} \frac{1}{2^p}$ irrational?

Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$

Prove that there exists at least one subset of the set $A=\{a_1,a_2,a_3,\dots,a_n\}$ such that the sum of its members is divisible by n.

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