By A CooperRecall that we defined inverses for any relation: Definition. If is a relation from to , then is a relation from to , defined by... |functions

By A CooperConsider the set of all functions . Each subset has such a function, namely its characteristic function, ; moreover, given we can define the set... |functions

By A CooperPushforwards and Pullbacks A function gives us a way of taking elements in and pushing them over to . We call the image of under... |functions

By A CooperSet Operations on Functions Functions are sets, so we can try to combine them like we combine sets. That is, we can ask the following... |functions

By A CooperWhen are two functions equal? A function is a kind of relation, which means it's a kind of set. So two functions being equal means,... |functions