Prove: Let S and T be sets. If there exists and injection from |S| --> |T| then there exists an injection from |P(S)|-->|P(T)|

(P(S) and P(T) represent the power sets of each)

Printable View

- September 22nd 2008, 07:47 AMGoldendoodleMomPower Sets
Prove: Let S and T be sets. If there exists and injection from |S| --> |T| then there exists an injection from |P(S)|-->|P(T)|

(P(S) and P(T) represent the power sets of each) - September 22nd 2008, 08:15 AMPlato
Here is a bit of notation.

That is called the image set of under .

Now it is clear that we have , so we must prove that if

Of course to do that you must show . - September 22nd 2008, 08:35 AMGoldendoodleMomPower Sets
The proof is regarding the cardinality of the sets and power sets. Does that change the strategy?

- September 22nd 2008, 08:43 AMPlato