Combinatorics | Mathematical principles | Theorems in discrete mathematics | Ramsey theory
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. For example, if one has three gloves (and none is ambidextrous/reversible), then there must be at least two right-handed gloves, or at least two left-handed gloves, because there are three objects, but only two categories of handedness to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, given that the population of London is greater than the maximum number of hairs that can be present on a human's head, then the pigeonhole principle requires that there must be at least two people in London who have the same number of hairs on their heads. Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip ("drawer principle" or "shelf principle"). The principle has several generalizations and can be stated in various ways. In a more quantified version: for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. For arbitrary n and m, this generalizes to where and denote the floor and ceiling functions, respectively. Though the most straightforward application is to finite sets (such as pigeons and boxes), it is also used with infinite sets that cannot be put into one-to-one correspondence. To do so requires the formal statement of the pigeonhole principle, which is "there does not exist an injective function whose codomain is smaller than its domain". Advanced mathematical proofs like Siegel's lemma build upon this more general concept. (Wikipedia).
What Is the Pigeonhole Principle?
The Pigeonhole Principle is a simple-sounding mathematical idea, but it has a lot of various applications across a wide range of problems. Learning to recognize pigeons and pigeonholes as they appear in different problems can help in discovering possible solutions. 0:00 Pigeonhole Princip
From playlist Spanning Tree's Most Recent
The Pigeonhole Principle (Proof by Contrapositive)
This video provides an informal proof of the Pigeonhole Principle using the method of proof by contrapositive. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Fundamentals of Mathematics - Lecture 32.2 : Proof of the Pidgeonhole Principle
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
PIGEONHOLE PRINCIPLE - DISCRETE MATHEMATICS
We introduce the pigeonhole principle, an important proof technique. #DiscreteMath #Mathematics #Proofs #Pigeonhole Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw
From playlist Discrete Math 1
3.5.1 The Pigeonhole Principle: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Discrete Math II - 6.2.1 The Pigeonhole Principle
In this video, we will explore the Pigeonhole Principle, which is a topic we didn't touch on in Discrete Math I. The concept itself it quite simple, stating that if we have more objects than places to put objects, then one of the places will have to have more than one object (paraphrased,
From playlist Discrete Math II/Combinatorics (entire course)
Fundamentals of Mathematics - Lecture 32.1: Pidgeonhole Principle - Applications
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html When I was an undergraduate at University of Arizona some of the post-docs there put together some great review sheets of techniques that are useful in competition problem solving. These will be posted on the course webpage for refere
From playlist Fundamentals of Mathematics
Mathsplanations: Pigeonhole Principle and Sock Picking
What do pigeons and socks have to do with each other? In this video we demonstrate the pigeonhole principle with a fun example - picking your socks in the dark! Another useful dose of Maths for everyone by Dr Sarada Herke. For more Math-y goodness check out my Graph Theory channel http:
From playlist Mathsplanations
The Pigeon Hole Principle: 7 gorgeous proofs
Let's say there are more pigeons than pigeon holes. Then, if all the pigeons are in the holes, at least one of the holes must house at least two of the pigeons. Completely obvious. However, this unassuming pigeon hole principle strikes all over mathematics and yields some really surprising
From playlist Recent videos
How Many Humans Have the Same Number of Body Hairs? | Infinite Series | PBS Digital Studios
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Do two people on the planet have the exact same number of body hairs? How about more than two? There’s a simple yet powerful mathematical principle that can help you fi
From playlist An Infinite Playlist
Total Functions in the Polynomial Hierarchy - Robert Kleinberg
Computer Science/Discrete Mathematics Seminar I Topic: Total Functions in the Polynomial Hierarchy Speaker: Robert Kleinberg Affiliation: Cornell University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
The Impossible Power of This Simple Math Proof
Sign up to Brilliant to receive a 20% discount with this link! https://brilliant.org/upandatom/ Recommended course: Infinity https://brilliant.org/courses/infinity/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upa
From playlist Math
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
[Discrete Mathematics] Pigeonhole Principle Examples
We do a couple pigeonhole problems, including a visual problem that requires a triangle. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?l
From playlist Discrete Math 1
We look at a formulation of the pigeonhole principle using functions. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.mi
From playlist Proof Writing