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September 29th, 2010, 04:29 AM   #1
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math analysis

Helllo every body this is my first questions in this forum and i expect to help ^^

Let f be a one-to-one function from A into B with B finite show that A is finite
Let f be a one-to-one function from A into B with B countable show that A is countable
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September 29th, 2010, 05:49 AM   #2
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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.
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September 29th, 2010, 02:58 PM   #3
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Re: math analysis

thank you parasio i really appreciate this
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September 29th, 2010, 05:17 PM   #4
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Re: math analysis

You're welcome. I hope you like the forum and continue to show up.
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