# injective functions

• May 31st 2008, 08:53 AM
skystar
injective functions
i got confused by this question seems relatively simple but dnt get it.
how many non-injective functions are there from {1,2,3,4} to {1,2,3,4,5}? How many non-injective functions are there from {1,2,3,4,5} to {1,2,3,4}?

thanks.
• May 31st 2008, 09:17 AM
Plato
Using a usual notation for sets of functions $\displaystyle B^A = \left\{ {f|f:A \mapsto B} \right\} \Rightarrow \quad \left| {B^A } \right| = \left( {\left| B \right|} \right)^{\left| A \right|}$, then if $\displaystyle A = \left\{ {1,2,3,4} \right\}\,\& \,B = \left\{ {1,2,3,4,5} \right\}$ there are $\displaystyle 5^4$ functions from A to B. Of those $\displaystyle (5)(4)(3)(2)$ are injections. So how many non-injections are there?

There are no injections from B to A. WHY?
• May 31st 2008, 09:28 AM
skystar
because B has more elements than A
when you say (5)(4)(3)(2)..what do you mean.thanks
• May 31st 2008, 09:32 AM
Plato
Quote:

Originally Posted by skystar
when you say (5)(4)(3)(2)..what do you mean.thanks

Multiply: (5)(4)(3)(2)=120!