Pigeonhole Principle Proof

by Agent M27
Tags: pigeonhole, principle, proof
Agent M27
Agent M27 is offline
May3-11, 09:46 PM
P: 171
1. The problem statement, all variables and given/known data

I have posted my proof of the Pigeonhole Principle.

2. Relevant equations

3. The attempt at a solution
Basically I am curious if this is an acceptable proof of the Pigeonhole Principle? I ask because both my professor and our textbook complete it differently, both of which make use of the restriction of a function. I choose this form for two simple reasons, I am having a hard time understanding why they are employing the restriction of a function and why they are employing the function g, but also this seems a lot simpler. I tend to make these things more difficult than they ought to be, but in mathematics nothing is arbitrary except the objects we place in sets. I have included both my version and the version my book used. My professor gave a proof similar to the one in the book. Thanks in advance. The first screenshot is my proof.

Attached Thumbnails
Pigeonhole.jpg   PigeonholeBook.jpg  
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)

Register to reply

Related Discussions
Pigeonhole Principle Calculus & Beyond Homework 1
Pigeonhole Principle Set Theory, Logic, Probability, Statistics 1
5.2 The Pigeonhole Principle pg.354 Calculus & Beyond Homework 1
Pigeonhole principle Calculus & Beyond Homework 12
Pigeonhole principle Calculus & Beyond Homework 17