2. Special Types of functions .o Definition 3.2: Let a be an arbitrary nonempty set The identity function on A, denoted by Ia, is defined by la(a=a Definition 3.3. Let f be an everywhere function from A to B. Then we say that f is onto(surjective ifRFB. We say that f is one to one(injective) if we cannot have fad-fa2) for two distinct elements a and az ofA. Finally, we say that f is one-to-one correspondence(bijection), if f is onto and one-to one . &o The definition of one to one may be restated in the following equivalent form 今If(a1)=f(a2) then a1=a2 for all a,a2∈AOr 令Ifa1≠a2 then j(a1)≠f(a2) for all a,a2∈A❖ 2. Special Types of functions ❖ Definition 3.2：Let A be an arbitrary nonempty set. The identity function on A, denoted by IA, is defined by IA(a)=a. ❖ Definition 3.3.: Let f be an everywhere function from A to B. Then we say that f is onto(surjective) if Rf=B. We say that f is one to one(injective) if we cannot have f(a1 )=f(a2 ) for two distinct elements a1 and a2 of A. Finally, we say that f is one-to-one correspondence(bijection), if f is onto and one-to￾one. ❖ The definition of one to one may be restated in the following equivalent form: ❖ If f(a1 )=f(a2 ) then a1=a2 for all a1 , a2A Or ❖ If a1a2 then f(a1 )f(a2 ) for all a1 , a2A