My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

Thanks Tree5Thanks
LinkBack Thread Tools Display Modes
February 24th, 2016, 08:39 PM   #11
Senior Member
Joined: Aug 2012

Posts: 2,385
Thanks: 745

Originally Posted by Polaris84 View Post
But I thought that all finite sets are countable? with 3 elements and 6 subsets, the pigeon hole principal applies, and the elements must repeat.
I'm suggesting that you walk through the proof step by step for a 3 element set with an 8 element power set. Write down the domain and range, pick some functions f, define the set X, show that X can't be hit by anything.

The pigeonhole principle doesn't apply at all here, you're mapping the smaller set to the larger set.
Maschke is online now  

  My Math Forum > College Math Forum > Number Theory

cantor, countability, natural, numbers, power, question, set, theorem

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Proof that Cantor's Theorem is Misunderstood krausebj0 Number Theory 206 July 9th, 2013 07:10 PM
power set of the natural numbers blabla Real Analysis 2 February 25th, 2012 01:31 PM
Disproof of Cantor's theorem krausebj0 Applied Math 6 November 29th, 2011 04:50 AM
Cantor's Theorem julian21 Number Theory 3 November 27th, 2010 10:47 PM
Cantor-Bendixson Theorem, uniqueness pascal4542 Applied Math 0 April 17th, 2010 09:49 AM

Copyright © 2019 My Math Forum. All rights reserved.