Thread: One-to-One Function Problem

Let A = {1,2,3}

(a) How many one-to-one functions are there from A to A?
(b) List all one-to-one functions onto A?

So far I have this:
(a) I believe the answer is 6, NOT SURE.

(b)
f1: A A
1 to 1
2 to 2
3 to 3

f2: A A
1 to 2
2 to 3
3 to 1

f3: A A
1 to 3
2 to 1
3 to 2

NOT SURE IF I ANM RIGHT? ANY HELP WOULD BE GREAT. THANK YOU!

Your answer of 6 is correct!
Then why do you just list 3?

Hi Plato,

I only listed three because that is all I could find. To me I have mapped each to one of the others one time and I don't see any more combinations. I know there should be three more, but I don't know what they would be? Thanks.

Here is a hint: 3!=6.
abc
acb
bac
bca
cab
cba

Originally Posted by Plato

Here is a hint: 3!=6.
abc
acb
bac
bca
cab
cba

I see what you mean. I am not sure how I would represent that like the other three functions above?

Originally Posted by Plato

Here is a hint: 3!=6.
abc
acb
bac
bca
cab
cba

I see what you mean. I am not sure how I would represent that like the other three functions above in just two columns?

I got it! the other three are:

f4:
A A
1 to 1
2 to 3
3 to 2


f5:
A A
1 to 3
2 to 2
3 to 1

f6:
A A
1 to 2
2 to 1
3 to 3

Originally Posted by MathStudent1

I got it! the other three are:

f4:
A A
1 to 1
2 to 3
3 to 2


f5:
A A
1 to 3
2 to 2
3 to 1

f6:
A A
1 to 2
2 to 1
3 to 3

Bravo! or is it brava? not sure if you're a guy or girl