- #1

kingwinner

- 1,270

- 0

**1) Prove that |NxR|=|R|**

I know how to prove that |R|

__<__|NxR|. But I am stuck at proving that |NxR|

__<__|R|. To prove this, I need a one-to-one function f: NxR ->R, but how can I find one?

**2) Prove that the cardinality of the set of all finite subsets of the xy-plane is c.**

Let S={all finite subsets of the xy-plane}

Let S_k={all finite subsets of the xy-plane with exactly k elements}

But I have some trouble understanding what S actually consists of. What I understand is that S contains points, lines, parabloas, etc.

S={ {(0,1), (5,8), (20,51)}, {y=2x+1 or y=x^2}, {y=2x^3}, ...}

How many elements are in {y=2x+1 or y=x^2}? 1 or 2?

Thank you for any help!