Give a partition of ω I have a question which I'm deeply confused about. I was trying to do some problems my professor gave us so we could practice for exam, one of them says:
Give a partition of  ω in  ω parts, everyone of them of cardinal  ω.
I know that $ ω=\left \{  1,2,3,...,n,n+1,.... \right \}$ , but I thought that |ω|=ω.
Can somebody help me?

You could for example write up the natural numbers in a kind of staircase pattern
1
...
1  3
2
...
1  3  6
2  5
4
etc (insired of course by the diagonal argument used to prove countability of the rationals)
then take every column as one of your sets.
