Give an example of a map

which is one-one but not onto

Dear Student

Let f: N→N, be a mapping defined by f (x) = x^2 –1
For f (x1) = f (x2)
Then, x1^2 – 1= x2^2 –1
x1=x2
Since x1+x2=0 is not possible

Further ‘f’ is not onto, as for 1∈N, there
f (x) = x^2 – 1 is not N.

Thanks