- #1
Bachelier
- 376
- 0
I'm trying to prove the following:
if E is infinite set and F is finite set. prove that E and E U F have the same
cardinality ?
So what I did:
I'm going to use Schroeder-Bernstein Thm.
1st, it's easy to show that |E| is less of equal to |E U F| since it is a subset of this latter.
Now I must show that |E U F| <= |E|
So I need to build an injection from E U F to E
Can I just define f(e) = e. Clearly this is 1-1 because if f(e1)= f(e2) then e1=e2. Hence |E U F| <= |E|
is this correct?
if E is infinite set and F is finite set. prove that E and E U F have the same
cardinality ?
So what I did:
I'm going to use Schroeder-Bernstein Thm.
1st, it's easy to show that |E| is less of equal to |E U F| since it is a subset of this latter.
Now I must show that |E U F| <= |E|
So I need to build an injection from E U F to E
Can I just define f(e) = e. Clearly this is 1-1 because if f(e1)= f(e2) then e1=e2. Hence |E U F| <= |E|
is this correct?