Prove |A-B|=|A|: An Uncountable Set Solution

[ranykar]

hello I am 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

 

[tiny-tim]

welcome to pf!

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]

tnx but that's not what i was asking.
i know that A-B is uncountable.
but how do i show 1:1 with A??

 

[Bacle2]

Try doing a reordering of A , so that B is an initial segment of A.

 

[tiny-tim]

http://en.wikipedia.org/wiki/Reductio_ad_absurdum

 

[Bacle2]

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