Please help on the followings.

1. Show that the following sets are denumerable (countably infinite)

(a) Q x Q (Q is the set of rational numbers) (This one is ok, but I am stuck at (b)

(b) Q($\displaystyle \sqrt(2)$) = {a+b$\displaystyle \sqrt(2)$ | a $\displaystyle \in$ Q and b $\displaystyle \in$ Q}

2. Show that (0,1) ~R(R is the set of reals)

3. Show that (0,1] ~ (0,1)

For 2 I simply could not think of the function from (0,1) toRthat is 1-1 onto. For 3, the existence of {1} is a problem. I could not find a 1-1 function that can deal with {1}.

Thanks!