Rationals Countability and Cantor's Proof - Gauge-institute.org

Gauge Institute, February 2006
H. Vic Dannon
2
2
2 2 6
1 .
The third line in the zig-zag has three rationals
3/1, 2/2, 1/3,
which are assigned as follows
3
3
1 2 9
1 ,
2
3
2 2 10
2 ,
1
3
3 2 11
3 .
The fourth line in the zig-zag has four rationals
1/4, 2/3, 3/2, 4/1
which are assigned as follows
1
4
1 2 17
4 ,
2
4
2 2 18
3 ,
3
4
3 2 19
2 .
4
4
4 2 20
1 .
The fifth line in the zig-zag has five rationals
5/1, 4/2, 3/3, 2/4, 1/5,
which are assigned as follows
5
5
1 2 33
1 ,
2
5
2 2 34
4 ,
6