- #36
kathrynag
- 598
- 0
HallsofIvy said:That's the hard way to do it! And, as I said before, what you are doing, looking at numbers of the form 1/n, is of no use because the integers are countable and none of these sets are countable.
As I said a long time ago, to define a one-to-one, onto function from [0,1] to (0,1)define f(x)= x for x any irrational number between 0 and 1, write all rational numbers in (0,1) in a list, r1, r2, etc. then define f(0)= r1, f(1)= r2, f(rn)= rn+2.
The hard way to do it is the way I was told to do it with proving [0,1) is equivalent to (0,1].