Thread: some play on empty sets

Hello

I just have some general question regarding functions. Consider the sets A and B. Now if , then the definition of the function fails but there is still a function , even though in both cases . So if we define as the set of functions from A to B, then if
, then



is that right reasoning ? I need this result in some proof.

Originally Posted by issacnewton

I just have some general question regarding functions. Consider the sets A and B. Now if , then the definition of the function fails but there is still a function , even though in both cases . So if we define as the set of functions from A to B, then if , then

is that right reasoning ? I need this result in some proof.

This question can start an argument. The emptyset is problematic.
That said, I will give a quote directly from Halmos.
If each of is a set and is the set of all functions then the quote
" has exactly one element, namely , whether is empty or not, and (ii) if is not empty, then is empty."

Plato, thats what I am saying too, am I not ?

Originally Posted by issacnewton

Plato, thats what I am saying too, am I not ?

I think so. But that notation is confusing.

Thats what Daniel (Velleman) uses in his book. Just following him.......