You have used the notation before. But it is not standard.
Does it mean If not please tell us how the textbook uses it.
Note that
So in this case .
Q 28 from page 26 of Combinatorics A Guided Tour:
Define g: by the rule g(S)=|S|, where S is any subset of [2]. Write g as a set of ordered pairs.
S could be {1} {2} and {1,2}.
So for S={1} would g(S) be 1? So would that be =2 and the ordered pair would be (2,1)?
But then for S={2} the cardinality of S would again be 1 giving the ordered pair (4,1).
I don't know how to do S={1,2}.
I am confused to the nth power.
Any clues towards unwarping my brain would be greatly appreciated.
Well you yourself said it does in the OP.
The function maps the subsets of
to the integers. The power set of is the set of all subsets of .
From the OP the function .
So it has everything to do with power sets.
But once again you notation is confused.
is the set of all functions from the set to the set .
However, that is not the way was defined.
If I were you, I would get a textbook that uses standard notation.
Yes, I see your point Plato. Thanks.
When it says any subset, then null would be one of those subsets.
I will have to ponder this and perhaps the professor will have time to expound on this. But since class hasn't started yet, perhaps he won't have time. Don't have a choice on the textbook however. Most of the text is very good, it's the unanswered problems that are a little fuzzy. I may try to pick up some extra material before the summer session starts.