no of onto function

juantheron · 2012-05-04 06:42:35

If a Set A consists of n- distinct elements, then total no. of onto function from A to A is

anonimnystefy · 2012-05-04 06:49:31

Because it is the same as the number of bijections from A to A,it will be n!

juantheron · 2012-05-04 06:54:26

yes

would you like to explain it to me

anonimnystefy · 2012-05-04 06:57:24

Do you understand why it is a bijection?

juantheron · 2012-05-04 07:14:33

no

anonimnystefy · 2012-05-04 07:29:37

If you had two elements that give us the same value,then there must be one of the other elements must give us two different values,which is a contradiction with the definition of a function. So all elements have there own value i.e. no two elements give us the same value of the function.This is the definition of a one-to-one function,and because it is an onto function,it is a bijection.

Math Is Fun Forum

#1 2012-05-04 06:42:35

no of onto function

#2 2012-05-04 06:49:31

Re: no of onto function

#3 2012-05-04 06:54:26

Re: no of onto function

#4 2012-05-04 06:57:24

Re: no of onto function

#5 2012-05-04 07:14:33

Re: no of onto function

#6 2012-05-04 07:29:37

Re: no of onto function

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