1. Write out in words what it would mean, according to Cantor, to say that A is
ID: 3147832 • Letter: 1
Question
1. Write out in words what it would mean, according to Cantor, to say that A is smaller than B and that B is smaller than A, i.e., that |A|<|B| and |B|<|A|.2. What is the resolution of the “fine point” that Cantor’s scheme leaves open?
3. What is the size of the set of points in the plane?
There is more to Cantor's scheme. He also introduced a way to say when one set is bigger another. A SUBSET of a set is a new set whose members all belong to the original set The subset is called PROPER if it doesn't have all the original members. Here is a set of 3 cards The next page shows 6 of the 8 proper subsets of this set. The only proper subset not shown is the empty set
Explanation / Answer
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1.|A|<|B| =Set A is smaller than set B when A is the same Size as a proper subset of B but not the same size as B.
|B|<|A|=Set B is smaller than set A when B is the same Size as a proper subset of A but not the same size as A.
2.resolution of the “fine point” that Cantor’s scheme leaves open
could it happen that there are sets A and B with |A|<|B| and |B|<|A|? if so then Cantor's notion of "size" is not much good .It wouldn't match our expectations of how that concept ought to behave
3.Size of set of point in the plane was 2^N0
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