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Ralph
2006-01-26 07:44:11

Wow! What an in-depth explanation for a gut-feel type solution. Here I go thinking like this:

(Assuming only integer values)

f(x,y)= x + y
f(x,y)= 1   -> impossible
f(x,y)= 2   -> x = 1 y = 1
f(x,y)= 3   -> x = 2y or y = 2x ... ehm ...
f(x,y)= 4   -> yeah, never mind.

f(x,y)= n   -> n = x + y  :-)

Ricky
2006-01-25 11:10:42

U told that THERE IS NO SUCH FUNCTION...SO CAN SUCH A FUNCTION COME???

Nope.  Never.  Not tomorrow, not in a million years.  Through the pigeon hole principle, we have shown that such a thing is impossible.  And unlike the matrix, there are no bending the rules in math, even in matrix math.

Any way let me know some personal thing about u???Are u a student??What do u do??

I'm a sophomore in college at Virginia Tech.  Right now, I'm a double math and computer science major.  The two complement each other nicely.  I use math in programming for things like modeling physical systems, and I use programming to solve some complex things in math.

soorejmg
2006-01-25 05:14:26

#### Ricky wrote:

I completely understand what you are saying.  But each element of A is two elements.

You have a function: f(x, y).  You can't just plug one number into that.  You have to plug two in.  Because of these, the elements in set A become (n, m), where n and m are from 0-255.

OHHHHHHHH..hurreehhhh I got it.......................

shooo do u know Ricky how i was thinking.....?I was thinking that if the two numbers comes in the same as (x,y) form there will only be 256 numbers.....sheyy.......It was a small mistake right?

GOT it now.....understud the pigeon hole principle also....

WAS A NICE HELP REALLY>>>RICKY>>>THANK U VERY MUCH>>>>

But again on emore thinggg..U told that THERE IS NO SUCH FUNCTION...SO CAN SUCH A FUNCTION COME???I FELT LIKE U HAVING SOME DOUBT IN THAT CASE>>WHAT WAS IT?

Any way let me know some personal thing about u???Are u a student??What do u do??

soorejmg
2006-01-25 04:33:20

#### Ricky wrote:

I completely understand what you are saying.  But each element of A is two elements.

You have a function: f(x, y).  You can't just plug one number into that.  You have to plug two in.  Because of these, the elements in set A become (n, m), where n and m are from 0-255.

Ricky
2006-01-25 04:05:36

I completely understand what you are saying.  But each element of A is two elements.

You have a function: f(x, y).  You can't just plug one number into that.  You have to plug two in.  Because of these, the elements in set A become (n, m), where n and m are from 0-255.

soorejmg
2006-01-25 02:30:49

That I agreee....But  if u have to say a function is onto and other such things etc  it might be individually applied to each member of set A and not  to two elemts together..Are u getting what i am asking?!!!!!!

Ricky
2006-01-25 01:52:04

Don't I get to sleep at all?

Listen to MathIsFun.  You aren't defining set A correctly.  Set A is _NOT_ [0, 255].  Set A is all of the possible combinations between two sets which are [0, 255].  Set A contains 65,536 elements.

soorejmg
2006-01-24 22:57:54

MathsIsFun
2006-01-24 20:20:44

OK, pigeonhole says "if there are more pigeons than holes, then some holes contain more than one pigeon"

So 256 holes with 65,536 pigeons means that some holes contain lots of pigeons.

soorejmg
2006-01-24 19:33:24

what has happened to every onee???no on ehere?

soorejmg
2006-01-24 16:05:28

#### Ricky wrote:

You are correct, f(x, y) is different than f(x) and f(y), but so is the explanation.

Remember, I never named the sets I was talking about in my explanation.  This is because it applies to every set and every function between those sets.

Let A = {(x, y) | x ∈ [0,255], y ∈ [0,255]}, the domain.  A is a set of ordered points, just like those in your function.  How many elements are in A?  255*255.

Let B = {z | z ∈ [0, 256]}, the range.

.

This one i understood.But not hat i asked.let A be the set above and B too.The connection between the domain and the range is through the function aplied on the domain set know?

This functions like onto  etc etc(i have studied it earlier dnt remember) comes when the FUNCTION is applied to each indiviual  member on domain.Here what is being done is the function is applied to two members of the set A.

so  how can it be?? Dnt kow if i am wrong..

MathsIsFun
2006-01-24 09:19:47

I am thinking about dice (because of another question on the forum): wouldn't it be the same as asking:

"I just threw two dice and the total was 8 ... what two dice did I throw?"

Ricky
2006-01-24 06:45:52

rickyoswaldiow, that only works for 3.

f(x, y) = x + y

f(x, y) = 15, what are x and y?

RickyOswaldIOW
2006-01-24 04:56:31

Maybe I don't fully understand the question but:
1+2=3

Ricky
2006-01-24 04:36:18

You are correct, f(x, y) is different than f(x) and f(y), but so is the explanation.

Remember, I never named the sets I was talking about in my explanation.  This is because it applies to every set and every function between those sets.

Let A = {(x, y) | x ∈ [0,255], y ∈ [0,255]}, the domain.  A is a set of ordered points, just like those in your function.  How many elements are in A?  255*255.

Let B = {z | z ∈ [0, 256]}, the range.

Now apply my previous post.

Good question, by the way.