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Uncountable sets need help 
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#1
Dec3012, 03:30 AM

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hello im struggled with a qustion
let B be a countable subset of uncountable set A. Prove AB=A i know how to prove that AB is uncountable but how do i show 1:1 with A? thanks ahead guys 


#2
Dec3012, 03:44 AM

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hello ranykar! welcome to pf!
(no, you're struggling with the question! or being strangled by it? ) hint: assume the opposite (ie, that AB is countable) 


#3
Dec3012, 03:49 AM

P: 2

tnx but thats not what i was asking.
i know that AB is uncountable. but how do i show 1:1 with A?? 


#4
Dec3112, 01:05 AM

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P: 1,169

Uncountable sets need help
Try doing a reordering of A , so that B is an initial segment of A.



#5
Dec3112, 04:45 AM

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P: 26,148



#6
Dec3112, 07:25 AM

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P: 1,169

I think s/he wants to set up an actual bijection between A and A\B .



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