Application of Pigeonhole Principle - non-constructive
28579
Creating a sequence that does not have an increasing or a decreasing sequence of length 3 from a set with 5 elements
28796
Use the Inclusion-Exclusion Principle to show that for any non-negative integers $m, r, n$ such that $m≤r≤n$...
65895
Irrationality proofs not by contradiction
87740
Pigeonhole Principle about division
102740
What are some important applications of the Erdős-Szekeres Theorem?
105221
Confusion about Satisfiability by a denumerable sequence.
3217
Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
113953
Circular permutations with indistinguishable objects
37331
Prove that every set with more than one element has a permutation without fixed points
65308
Axiom of Choice: Family of non-empty sets mutually disjoint or not?
7919
The pigeonhole principle - how to solve questions like that?
63538
Impossibility of constructing a continuum-size linearly independent set in $\Bbb R$
91485
Finding an uncountable chain of subsets the integers
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
88099
Not $\sigma$-compact set without axiom of choice
72371
Proof of Strong Induction Using Well-Ordering Principle
27448
The Collatz conjecture algorithm applied to negative integers