Let A be the set of all 50 students of Class X in a school. Let f : A → N be function defined by f(x) = roll number of the student x. Show that f is one-one but not onto.

Class 12, NCERT Chapter 1,  Example7

No two different students in the class can have the same roll number.
Therefore, f must be one-one.
We can assume without any loss of generality that roll numbers of students are from 1 to 50.
This implies that 51,52,53... in N is not roll number of any student of the class, so that 51,52,53...
 can not be an image of any element of X under f.
Hence, f is not onto.