







Countable and uncountable sets 
20070724 

From Mac: 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 ? Answered by Harley Weston. 





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

From Geetha: Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Answered by Penny Nom. 





A countably infinite collection of countably infinite sets 
20050226 

From Feroz: 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? Answered by Penny Nom. 





Subsets of a countably infinite set 
20011114 

From Tania: 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? Answered by Claude Tardif. 

