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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

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.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**soorejmg****Member**- Registered: 2006-01-20
- Posts: 24

Where is Ricky???RICKY please help me....

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**soorejmg****Member**- Registered: 2006-01-20
- Posts: 24

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?!!!!!!

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**soorejmg****Member**- Registered: 2006-01-20
- Posts: 24

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.

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**soorejmg****Member**- Registered: 2006-01-20
- Posts: 24

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??

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Ralph****Guest**

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 :-)