I have recently got acquainted with a special kind of function known as a set function . I've a series of questions in my mind with respect to this .
Firstly it is hard on my part, at this level to have an understanding of set function. It is defined as a function which takes an input a set and gives a number as output. First of all I'm not able to grasp how a set can be taken as input and above that how can it give a number as a output. So I want anyone to explain me clearly what a set function is and how it works.
The next thing is that I'm unable to find examples of a set function . One example that I could partially understand is that the function that gives a set its cardinality is a set function . I said that I could partially relate to this is as I could not understand how this would be a function. I also searched this on Wikipedia but the examples they gave were beyond my level of understanding. So I would be highly thankful if someone give me examples of set function but I don't want complicated one's which are beyond my thinking.
Lastly I want to ask how area is a set function and does it have infinite sets as domain. In general I want to know how area is a set function .
Thanks in advance for any possible help.