Originally Posted by

**spearfish** Hey all,

I am getting stuck proving the following relation:

x, y are elements of Q^+. x~y iff x = y(2^n) for some integer n.

Here's what I have so far:

Reflexive:

Let x be an element in Q^+.

x = x(2^n).

x/x = 2^n

1 = 2^n

1 = 2^0

1 = 1, Ok so does this prove xRx or do I need further work?

*Symmetric:*

Let x,y be elements in Q+.

Suppose xRy.

x = y(2^n)

Now suppose yRx.

y = x(2^m)

Plugging in for y and solving for x, I get

x = (x(2^n))(2^m)

x = x(2^n+m)

x/x = 2^(n+m), This is what I don't know what to do. What exactly does this result tell me? Do I need further work, or is this completely the wrong approach? Please somebody.

Transitive:

Let x,y,z be elements in Q+

Suppose xRy.

x = y(2^n)

Suppose yRz.

y = z(2^m).

Pluggin in and solving.

x = (z(2^m))(2^n)

x = z(2^m+n), Once again, now what?

Please explain my faults and show how to correct. Explanations would be very helpful. Thanks