Register to reply

Uncountable sets need help

by ranykar
Tags: cardinal, countable, power, uncountable
Share this thread:
ranykar
#1
Dec30-12, 03:30 AM
P: 2
hello im struggled with a qustion
let B be a countable subset of uncountable set A.
Prove |A-B|=|A|
i know how to prove that A-B is uncountable
but how do i show 1:1 with A?

thanks ahead guys
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
tiny-tim
#2
Dec30-12, 03:44 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
hello ranykar! welcome to pf!

(no, you're struggling with the question!
or being strangled by it? )


hint: assume the opposite

(ie, that A-B is countable)
ranykar
#3
Dec30-12, 03:49 AM
P: 2
tnx but thats not what i was asking.
i know that A-B is uncountable.
but how do i show 1:1 with A??

Bacle2
#4
Dec31-12, 01:05 AM
Sci Advisor
P: 1,170
Uncountable sets need help

Try doing a reordering of A , so that B is an initial segment of A.
tiny-tim
#5
Dec31-12, 04:45 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
http://en.wikipedia.org/wiki/Reductio_ad_absurdum
Bacle2
#6
Dec31-12, 07:25 AM
Sci Advisor
P: 1,170
I think s/he wants to set up an actual bijection between A and A\B .


Register to reply

Related Discussions
Sets of all functions. Countable and Uncountable sets. Calculus & Beyond Homework 1
Uncountable sets and forcing Set Theory, Logic, Probability, Statistics 2
Uncountable union of a chain of countable sets can be uncountable? Set Theory, Logic, Probability, Statistics 11
Countable, uncountable sets Calculus & Beyond Homework 1
Uncountable sets Calculus & Beyond Homework 5