Simple problem from

Amazon.com: Discovering Modern Set Theory. I: The Basics (Graduate Studies in Mathematics, Vol…
We define a function G from [0, 1) x [0, 1) to [0, 1) as follows:

For any <x, y> in [0, 1) x [0, 1) such that x = 0.x1x2x3x4x5... and y = y1y2y3y4y5... G(x, y) = 0.x1y1x2y2x3y3....

Clearly this is into. However, in the book they claim it is not onto. I can't see why this is. My reasoning is:

Take any z in [0, 1) such that z = 0.z1z2z3z4z5.... then x = 0.z1z3z5z7... and y = 0.z2z4z6z8... will be such that G(x, y) = z.

Any help would be great.

Regards

Sam