# Type Theory Question

1. Apr 7, 2009

### mXSCNT

In type theory, what is the difference between the set of functions $$A \rightarrow B$$ and the implication set $$A \supset B$$? Is there any difference? My text says that both of them are examples of sets (propositions) that are defined as special cases of the cartesian product $$\prod(A,B)$$ (this cartesian product is the set of functions $$f(x)$$ from the index set $$A$$ to $$B(x)$$ where the image of $$x$$ lies in a set $$B(x)$$ that is itself dependent on $$x$$).