3) Prove that the cardinality of the open unit interval, (0,1),
is equal to the cardinality of the open unit cube:
{(x,y,z) E R^3|0<x<1, 0<y<1,
0<Z<1}.
[Hint: Model your argument on Cantor's proof for the
interval and the open square. Consider the decimal expansion of the
fraction 12/999. It may prove handdy]