Question

Give an example for a function from the set of integers to the set of positive integers that is injective, but not surjective.

Answer 1

Injective means we won't have two or more "A"s pointing to the same "B".

Injective is also called "One-to-One"

Surjective means that every "B" has at least one matching "A" (maybe more than one).

There won't be a "B" left out.

A=Z

B=Z⁺

The function f is one to one. i.e. injective. as f(a)=f(b) implies a=b

the function f is not surjective. For eg: 2 can not be written as 3x or 3|x|+1.