Let f:N <span lan

Given: f (n) = (n + 1)/ 2, if n is odd

n/ 2, if n is even

Case 1: When n is odd,

When n = 1,

When n = 3,

When n = 2k – 1, … (1)

Case 2: When n is even,

When n = 2,

When n = 4,

When n = 2k, … (2)

When n = 2n, … (3)

From (1) and (2),

⇒ f (2k – 1) = f (2k)

∴ f is not one – one.

From (3),

⇒ f (2n) = n

∴ f is onto.

∴ f is onto but not one – one.

Hence f is not bijective.