Re: empty set and functions

Quote:

is it correct reasoning ?

You are absolutely right.

To go a little further, consider the following definition. A set *A* is called initial if for every set *B*, there is one and only one function from *A* to *B*. Then the empty set is the unique initial set.

Re: empty set and functions

thanks makarov, I have finished first 4 chapters of Daniel Velleman's "How to prove it" and going to the fifth chapter , Functions. Since I am familiar with all the logical

machinery , it was easy to draw the conclusion I drew. If somebody has only calculus background , then it will be difficult for that person to see why there is a function from A to B , when A is an empty set......... By the way , I just downloaded (Rock)a beautiful book on set theory , "The Joy of sets:Fundamentals of contemporary set theory" by Keith Devlin and since I have already studied basic logic , its really joy to read it....