1. ## Functions...

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 $\rightarrow$ N that is injective. Define the function by giving a rule for it, i.e., (f(x)=...)

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

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

2. Originally Posted by 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 $\rightarrow$ 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 $\rightarrow$ 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
This is trivial.

Tonio

3. This is really trivial stuff. Make sure you understand what is meant by an injective function, and a surjective function and the rest is easy.

4. Ya know what I'm gonna post an answer here because despite all the books and lectures I've been to its taken me forever to understand injections and stuff.

Here's an example of an injection.
Let A = {1,2,3}, B = {1,4,9,16}
then for an element x in A we can find a corresponding element in B by squaring x. So for x=1 which is in A, if we square it we get 1 which is in B. For x=2 we get $2^2 = 4$ etc... So its really just finding a 'formula' that will transfer one element of a set to another.

Note that the amount of elements in B has to be greater than or equal to the amount of elements in A which should help with part c)...

5. ## Thanks

Thanks to those who have helped. I know that, to you, the questions I am posting might be trivial. However, I am coming back to taking math classes after 15 years. I am struggling with this class because the lectures are nothing like the homework assignments. I was good in math when I was taking the classes, but I have a lot of catch up to do.