- #1
calvino
- 108
- 0
Proof for similarity between R X R, and R...
Well, there are actually two similar questions that I need help on. The first is to prove that for any infinite set R, there is always a 1-1, and onto mapping from RxR to R.
The second is to show that (RXR, +) ~ (R, +). Here R is the reals, and ~ symbolizes that the two are isomorphic.
I know the two questions are similar, which is why I grouped them together. I'm just not sure where to start. Any help would be great, and I'll be sure to post my progress. Thanks
Well, there are actually two similar questions that I need help on. The first is to prove that for any infinite set R, there is always a 1-1, and onto mapping from RxR to R.
The second is to show that (RXR, +) ~ (R, +). Here R is the reals, and ~ symbolizes that the two are isomorphic.
I know the two questions are similar, which is why I grouped them together. I'm just not sure where to start. Any help would be great, and I'll be sure to post my progress. Thanks