# One-to-One Function Problem

• Feb 27th 2007, 04:00 PM
MathStudent1
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!
• Feb 27th 2007, 04:08 PM
Plato
Then why do you just list 3?
• Feb 27th 2007, 04:10 PM
MathStudent1
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.
• Feb 27th 2007, 04:15 PM
Plato
Here is a hint: 3!=6.
abc
acb
bac
bca
cab
cba
• Feb 27th 2007, 04:17 PM
MathStudent1
Quote:

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?
• Feb 27th 2007, 04:19 PM
MathStudent1
Quote:

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?
• Feb 27th 2007, 05:08 PM
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
• Feb 27th 2007, 06:09 PM
Jhevon
Quote:

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