Quandaries and Queries
  

 

Name: Lisa

First-year college question
Status: I'm a student

A function that is onto but not one-to-one where f:N-->N

Thanks so much!
 

 

Hi Lisa,

I assume that N is the natural numbers, 1,2,3,... I am going to distinguish between the two copies of N by writing one N and the other N. You want a function from f:N -> N which is onto but not one-to-one.

Onto means that every number in N is the image of something in N. One-to-one means that no member of N is the image of more than one number in N. Your function is to be "not one-to-one" so some number in N is the image of more than one number in N. Lets say that 1 in N is the image of 1 and 2 from N. That is

f(1) = 1 and f(2) = 1 Now to be "onto" all of the other numbers in N; 2,3,4,..., must be the image of something from N. In N you are left with 3,4,5,... so you could map 3 to 2,
4 to 3,
5 to 4,
... That is f(n) = n-1 if n is larger than 2.

Penny 		 
 

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