# Math Help - cardinals

1. ## cardinals

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2. Originally Posted by yellow4321
i just want to check im doing this right because it seems too easy
the question asks for the cardinals of the sets A {5,6} and B {1,2,3}, i said 2 and 3 respectively. then i assumed |AxB|=2.3=6. just looking for some verification?
you are correct

3. Originally Posted by yellow4321
i just want to check im doing this right because it seems too easy
the question asks for the cardinals of the sets A {5,6} and B {1,2,3}, i said 2 and 3 respectively. then i assumed |AxB|=2.3=6. just looking for some verification?
Cardinal values of finite sets are easy.

The cardinality of infinite sets is not so easy.

-Dan

4. Originally Posted by topsquark
The cardinality of infinite sets is not so easy.

-Dan
don't i know it!

working with infinite sets defies logic sometimes... or maybe our logic just isn't up to the standard

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6. Originally Posted by yellow4321
(sorry for posting in elementary math forum,i dont know how to move thread)
you should create a new thread for new questions

7. Originally Posted by yellow4321
clearly theres much passion for this topic,i now need help with an introductory question on schroder-berstein theorem. Let X,Y be finite sets with |X|=n and |Y|=m show n is 'less than or equal to m' then there is a injection X->Y.
First, don’t be concerned about the statements on cardinality.
Once you have the basic idea down, all the rest is easy.

Secondly, the above is not the Schroeder-Bernstein. But nonetheless it is easy to prove anything about finite sets.
The basic idea of a finite set is: Any finite set can be listed using positive integers as subscripts.

Thus if $n = \left| X \right| \le \left| Y \right| = m$ then we can write $X = \left\{ {x_1 ,x_2 ,x_3 , \cdots ,x_n } \right\}\,\& \,Y = \left\{ {y_1 ,y_2 ,y_3 , \cdots y_m } \right\}$.

If we define $f:X \mapsto Y$ by $f\left( {x_j } \right) = y_j$ the result follows easily.

8. .. for all x,y in X f(x)=f(y) then x=y ?
the less than/equal to sign is confusing me.

9. Originally Posted by yellow4321
.. for all x,y in X f(x)=f(y) then x=y ?
the less than/equal to sign is confusing me.
It is easy. The m terms of Y are all distinct.