# number of functions

• May 16th 2010, 09:35 AM
hmmmm
number of functions
if i am asked the number of functions between {1,2,3}-> {1,2,3} then as the cardinality is the same all injective functions will be bijective and so also surjective and there are 6 of these, however i am given a formula that states the number of functions between two sets is X -> Y is |X|^|Y| which gives me 27 what have i done wrong here?
• May 16th 2010, 10:10 AM
Plato
Quote:

Originally Posted by hmmmm
if i am asked the number of functions between {1,2,3}-> {1,2,3} then as the cardinality is the same all injective functions will be bijective and so also surjective and there are 6 of these, however i am given a formula that states the number of functions between two sets is X -> Y is |X|^|Y| which gives me 27 what have i done wrong here?

I am not at all sure that I understand what you are asking.
But if $B=\{1,2,3\}$ then there are $3^3$ functions $f:B\to B$.
Of those 27 functions there $3!=6$ of them which are bijections.
So what is your question now?
• May 16th 2010, 10:23 AM
hmmmm
well the six functions would be injective and surjective, so are the other 21 functions neither injective or surjective?
thanks the help