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

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<strong>Gauge</strong> Institute, February 2006<br />

H. Vic Dannon<br />

2<br />

2<br />

2 2 6<br />

1 .<br />

The third line in the zig-zag has three rationals<br />

3/1, 2/2, 1/3,<br />

which are assigned as follows<br />

3<br />

3<br />

1 2 9<br />

1 ,<br />

2<br />

3<br />

2 2 10<br />

2 ,<br />

1<br />

3<br />

3 2 11<br />

3 .<br />

The fourth line in the zig-zag has four rationals<br />

1/4, 2/3, 3/2, 4/1<br />

which are assigned as follows<br />

1<br />

4<br />

1 2 17<br />

4 ,<br />

2<br />

4<br />

2 2 18<br />

3 ,<br />

3<br />

4<br />

3 2 19<br />

2 .<br />

4<br />

4<br />

4 2 20<br />

1 .<br />

The fifth line in the zig-zag has five rationals<br />

5/1, 4/2, 3/3, 2/4, 1/5,<br />

which are assigned as follows<br />

5<br />

5<br />

1 2 33<br />

1 ,<br />

2<br />

5<br />

2 2 34<br />

4 ,<br />

6

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