







Countable and uncountable sets 
20070724 

Mac pose la question : Hi, i tried to read few webpages related to the countably infinite and uncountable sets.
Even i read few questions from this forum.
But i am not convinced with this explanation. If you have any good book that
explains this in layman term, please redirect me to that.
1) Can you please explain what is the difference between these too ?
2) How could you say set of Natural number and set of even numbers are countably
infinite ?
N={1,2,3,...} and Even= {2,4,6,...}
When an element in the even set is some 2n, we will map it to 'n'.So
now we have a bigger number(2n) right ?
Sorry, i didn't understand that.
...
Can you please help me out to understand that ? Harley Weston lui répond. 





The cartesian product of a countably infinite collection of countably infinite sets 
20060325 

Geetha pose la question : Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Penny Nom lui répond. 





A countably infinite collection of countably infinite sets 
20050226 

Feroz pose la question : Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set? Penny Nom lui répond. 





Subsets of a countably infinite set 
20011114 

Tania pose la question : How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Claude Tardif lui répond. 

