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Uncountable sets need help

by ranykar
Tags: cardinal, countable, power, uncountable
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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
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tiny-tim
#2
Dec30-12, 03:44 AM
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P: 26,160
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: 1,169
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
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http://en.wikipedia.org/wiki/Reductio_ad_absurdum
Bacle2
#6
Dec31-12, 07:25 AM
Sci Advisor
P: 1,169
I think s/he wants to set up an actual bijection between A and A\B .


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