# Function notation

1. Jun 14, 2010

### ballzac

1. The problem statement, all variables and given/known data
Give an example of a map from the set N of positive integers to itself which
is surjective but not injective.

2. Relevant equations

3. The attempt at a solution
It's easy to come up with an example, but I'm not sure on notation.
Here's how I've written it, but I know it's not quite right. I'm sure you can see the function that I am meaning to give. Any help with the notation would be appreciated. If it's not clear what function I mean, let me know and I will put it into words :)

$$\lbrace f:f(1)=1, f(s)=s-1,s>1\rbrace$$

2. Jun 14, 2010

### Dick

That's plenty clear enough. Just defining f(1)=1 and f(s)=s-1 for s>1 without using the {} notation is also fine.

3. Jun 14, 2010

### ballzac

Oh cool. Thank you for your quick response. I may actually just define the function as you say and use words to explain it if it comes up in the exam. I think the lecturer prefers things explained as much in words as possible anyway.

4. Jun 14, 2010

### Dick

That's plenty clear enough. Just defining f(1)=1 and f(s)=s-1 for s>1 without using the {} notation is also fine.