Countability - Math Help Forum

$Math Help Forum$

$Go Back$		Math Help Forum > University Math Help > Other Advanced Topics
$Reload this Page$ Countability

Download MHF Flyer

Mark Forums Read

$Reply$

#1

$Old$ November 28th, 2008, 12:09 PM

jas_viru $jas_viru is offline$

Newbie

Join Date: Nov 2008

Posts: 1

Country:

India

Thanks: 0

Thanked 0 Times in 0 Posts

$jas_viru is on a distinguished road$

$Default$ Countability

Q:
Let A,B≠0 and let f:A→B be an onto mapping. Then if A is countable then prove B is countable.

$Reply With Quote$

Advertisement

#2

$Old$ November 28th, 2008, 12:49 PM

Plato $Plato is online now$

MHF Contributor

Join Date: Aug 2006

Posts: 6,537

Thanks: 64

Thanked 2,414 Times in 2,210 Posts

$Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$ $Plato has a reputation beyond repute$

$Default$

Quote:

Originally Posted by jas_viru $View Post$

Q:
Let A,B≠0 and let f:A→B be an onto mapping. Then if A is countable then prove B is countable.

This is one of the most important theorems in theory of cardinality of sets: $f: A \mapsto B \text{ is onto if and only if there is a one-to-one } g: B\mapsto A$ .
Now any subset of a countable set is countable. Because $g(B)\subset A,\; g(B)\text { is countable }$

That means that $B \text{ is countable }$ .

$Reply With Quote$

The following users thank Plato for this useful post:
GaloisTheory1
$Donate to MHF$

$Reply$

« Linear programming - Polygon packaging | Top | Proving connected/compact »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 03:56 PM.

your link here Sponsors

rv solar, e-learning,

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.