Bijective Function

(Bijection) #

A function f:A→B is bijection if ‘f’ is:

1. One-one (Injective)
2. Onto (Surjective)

If f:A→B is bijective, |A|=x and |B|=y,

• By one-one: x≤y
• By onto: x≥y
• ∴ x=y

Number of bijective functions possible #

If f:A→B is one-to-one, |A|=x and |B|=y, x=y=n number of functions possible = $n*(n-1)*(n-2)…(1)=n!$