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**minkyboodle** This 3 part problem deals with functions from the set P of cell phones in use in the US to the set of natural Numbers **N.**

a) Write one interesting function *f:P$\displaystyle \rightarrow$ ***N** that is injective. Define the function by giving a rule for it, i.e., (f(x)=...)

To each person with a cell phone in the US attach a number n in N, so taht we can speak of person 1, person 2, etc.

Define f: P --> N by f(x) = the owner of x

b) write a function *f:P$\displaystyle \rightarrow$ ***N **that is not injective. Again, give a rule

Now come up with a fucntion that maps each phone to the company that sold it...

c) Explain why there is no function from P to N that is surjective