September 29th, 2010, 05:29 AM  #1 
Newbie Joined: Sep 2010 Posts: 18 Thanks: 0  math analysis
Helllo every body this is my first questions in this forum and i expect to help ^^ Let f be a onetoone function from A into B with B finite show that A is finite Let f be a onetoone function from A into B with B countable show that A is countable 
September 29th, 2010, 06:49 AM  #2 
Senior Member Joined: Feb 2009 Posts: 172 Thanks: 5  Re: math analysis , finite. Since and is finite we have that is finite. Consider the function defined as for all . We have that is an injection since is an injection and we have that is surjective since for all there exists such that . Hence is a bijection from to and then since is finite is finite. , countable. Since and is countable we have that is countable. Consider the function defined as for all . We have that is an injection since is an injection and we have that is surjective since for all there exists such that . Hence is a bijection from to and then since is countable is countable. 
September 29th, 2010, 03:58 PM  #3 
Newbie Joined: Sep 2010 Posts: 18 Thanks: 0  Re: math analysis
thank you parasio i really appreciate this

September 29th, 2010, 06:17 PM  #4 
Senior Member Joined: Feb 2009 Posts: 172 Thanks: 5  Re: math analysis
You're welcome. I hope you like the forum and continue to show up.


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