- #1
kingwinner
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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!
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!