Question about domain of problem

[Bdanielz]

Disclaimer this is homework, but just s small piece of a larger problem.

I have built my code to get gcd... using bigint
What I need help with is making sure the range of my problem set

Given

    x,y∈ℤ
     1≤x≤2^500
     1≤y≤2^500
     x>y

I need to compare combinations of the above.
let y = column one and x = column two

1^1  through  1^500 

      and 

2^1  through  2^500 

      and

2^1  through  1^500 
1^500 through 2^500 

cover the entire range my possible solutions?

[TheIdeasMan]

Hi,

if ^ means exponent, then:

1^500

is 1 :+)

and 2^1 is 2 :+)

So your range is 1 -> 2^500, yes?

Maybe I misunderstood?

[Bdanielz]

I think your correct.

[Bdanielz]

So I know I need

1^1 through 1^500

and

2^1 through 2^500


but is

2^1 through 1^500
1^500 through 2^500

commutative ? do I only need

2^1 through 1^500

[TheIdeasMan]

Sorry, but I am not understanding.

but is

2^1 through 1^500
1^500 through 2^500

commutative ?

Translating, that is:
is

2 through 1
1 through 2^500

commutative ?

I don't understand how you came up with your ranges: 1≤x≤2^500 means x is between 1 and 2^500. How did you arrive at 1^500? Especially, given that 1^500 is 1?

Why do you want to know whether it is commutative, given that x > y ?