- #1
georgetown13
- 7
- 0
Homework Statement
Let U be a countable set. For j=1, 2, 3, ... define
Fj= {(x1, x2, ... , xj): xi [tex]\in[/tex] U for all i=1,2,...,j}
Prove that j=1,2,3,...,Fj is countable.
Homework Equations
The Attempt at a Solution
I'm having trouble understanding what the set Fj contains.
F1={x1}
F2={x1, x2}
And so on...
But as xi for all i=1,2,3,...,j is in U, does that mean Fj is a subset of U?
Does this mean that I have to prove that if a set is countable, its subset is countable?
If so, how would I go about doing that?
Please help! I would greatly appreciate it. I'm having a hard time just understanding the question at all.