Question

how can i calculate how many onto functions are between two sets

Answer 1

V={1,2,3,4,5} and W={x,y}

Answer 2

well nice problem it's not easy though ;)

Answer 3

i knowww
:(

Answer 4

thats why i cant do it:(

Answer 5

you want to count for that particular set or in general ?

Answer 6

those two sets only

Answer 7

i got the trick... 5 element goes to x the 4 goes to y then 3 goes to either x or y then 2 goes to either x or y then 1 goes to either x or y

Answer 8

im good?

Answer 9

Hmm You can use mutual inculusion exclusion or use the stirling number of second kind in general http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind

Answer 10

yea... but he didnt teach non of those methods

Answer 11

He won't this is a difficult problem,he will probably want you to use mutual incusion exclusion but that's time consuming and error-prone. Just remember this formula

If A,B are non-empty sets of cardinality m,n with \[ m \ge n \].Then there are $$\sum_{i=0}^{(n-1)} (-1)^i {n \choose i} (n-i)^m \text{ onto functions in } f \colon A \to B $$

Answer 12

i dont like series do
what would be i

Answer 13

what ?

Answer 14

which class are you in ?

Answer 15

thats sum....

Answer 16

i dont know how to work with it...

Answer 17

decrete mathematics
the beginning

Answer 18

Undergraduate classes?

Answer 19

am doing relations, venn diagrams.. yea

Answer 20

yea

Answer 21

If an undergraduate student don't understand summation,then I have nothing to say any more...

Answer 22

well i didnt do it yet

Answer 23

so ur expecting that the people come here already know everything?