Thread: Hausdorff dimension of sets

What is the Hausdorff dimension of the following sets?

a) { (x,x) R^2 : x Q } where R is the real numbers and Q is the rational numbers.

b) { (x,x) R^2 : x R }

c) { (x,x)R^2 : x C } where C is the middle third cantor set.



I think the answer to c) is log2/log3 but i am not sure how to find the other two Hausdorff dimensions.

Thanks.

Perhaps because they are so trivial!
The Hausdorf dimension of the points in R^2, both of whose coordinates are rational, is 0 because that set is countable.

The Hausdorf dimension of all of the points in R^2 is 2.