(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 :-)

]]>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.

]]>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??

]]>]]>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.

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.

]]>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.

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

]]>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..

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

]]>f(x, y) = x + y

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

]]>1+2=3]]>

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.

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