Quote:
Originally Posted by TheRekz  Give an example of a function from N to N that is one to one but not onto
My answer is the function from {a,b,c} to {1,2,3,4} with f(a) = 3, f(b) = 4, f(c) = 1. Is this the correct example to this question? What does it mean from N to N? |
No it is not correct.
First N is the set of counting numbers either {0,1,2,3,...} or {1,2,3,4,...} (i.e. it contains 0 or not depending on your textbook). So N is infinite; so your example must be infinite also. Here is another example in addition to the one given above.
![f:N \mapsto N,\quad \left( {n \in N} \right)\left[ {f(n) = 2^n } \right]\quad](http://www.mathhelpforum.com/math-help/latex2/img/8e2fcc2fbefef0a1aa3f893aeee32af3-1.gif "f:N \mapsto N,\quad \left( {n \in N} \right)\left[ {f(n) = 2^n } \right]\quad")