1. The problem statement, all variables and given/known data Let a,b[tex]\in[/tex][tex]\Re[/tex] such that a < b. Show |(a,b)|=|(0,1)| and Show |(0,1)|=|(0,[tex]\infty[/tex])| 2. Relevant equations 3. The attempt at a solution] I know that |(0,1)| is equal to the continuum and has the same cardinality as the reals. I would guess that |(0,[tex]\infty[/tex])| is also equal to the continuum. My second educated guess is that since a < b, there are an infinite amount of reals in between a and b also, therefore |(a,b)| is equal to the continuum, too. I might be wrong there. I know that two sets have the same cardinality if I can find a one-to-one function from one to the other. I feel like I know more than I am saying here but I cannot really come up with anything. Is it always necessary to come up with a function? The examples that I have look very hard to come up with. Thank you all, in advance.