Welcome to C.H. Explained

Ted William Griffin's

Continuum

Hypothesis

solution

The Continuum Hypothesis (CH) states that all sets of infinity are the same size.

If you take an infinite set of Numbers and pair them up with another set of infinite Numbers the sets appear to be the same size.  Example (1,2,3,4,5,6,7,8, 9, ... & 10,20,30,40,50,60,70,80,90...)

It was taken even further to fractions and a graph was made.

1/1  1/2  1/3  1/4  1/5  1/6  1/7  1/8  1/9  ...

2/1  2/2  2/3  2/4  2/5  2/6  2/7  2/8  2/9  ...

3/1  3/2  3/3  3/4  3/5  3/6  3/7  3/8  3/9  ...

4/1  4/2  4/3  4/4  4/5  4/6  4/7  4/8  4/9  ...

5/1  5/2  5/3  5/4  5/5  5/6  5/7  5/8  5/9  ...

6/1  6/2  6/3  6/4  6/5  6/6  6/7  6/8  6/9  ...

7/1  7/2  7/3  7/4  7/5  7/6  7/7  7/8  7/9  ...

8/1  8/2  8/3  8/4  8/5  8/6  8/7  8/8  8/9  ...

9/1  9/2  9/3  9/4  9/5  9/6  9/7  9/8  9/9  ...

...     ...     ...     ...     ...     ...     ...     ...     ...     ...

 Then a zig zag line was draw and stretched out to pair this graph with another infinite set to show them as the same size.

example

1/1  1/2  1/3  1/4  1/5  1/6  1/7  1/8  1/9  ...

2/1  2/2  2/3  2/4  2/5  2/6  2/7  2/8  2/9  ...

3/1  3/2  3/3  3/4  3/5  3/6  3/7  3/8  3/9  ...

4/1  4/2  4/3  4/4  4/5  4/6  4/7  4/8  4/9  ...

5/1  5/2  5/3  5/4  5/5  5/6  5/7  5/8  5/9  ...

6/1  6/2  6/3  6/4  6/5  6/6  6/7  6/8  6/9  ...

7/1  7/2  7/3  7/4  7/5  7/6  7/7  7/8  7/9  ...

8/1  8/2  8/3  8/4  8/5  8/6  8/7  8/8  8/9  ...

9/1  9/2  9/3  9/4  9/5  9/6  9/7  9/8  9/9  ...

...     ...     ...     ...     ...     ...     ...     ...     ...     ...

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

& 

1/1, 1/2, 2/1, 3/1, 2/2, 1/3, 1/4, 2/3, 3/2, 4/1, ... 

but when decimals were attempted to be graphed the graph was incomplete.

Until now!

I am about to teach you how to graph any rational decimal number!

First you have to look at a decimal any decimal number to understand what is happening there are FIVE infinities!

Start point 0.0

A.BCD

The first two infinities are represented by A it goes infinitely in both directions positive and negative.

The next infinity is represented by B it stands for the total number of zeros between the decimal and the first nonzero integer past the decimal.

the next infinity is represented by C it is the number starting with the first nonzero integer after the decimal to the last nonzero integer. Example (0.0123 C=123)

The final infinity is the total number of zeros at the end of the number after the last nonzero integer.

  Now that you understand how to read a number this way it is time to find you Numbers coordinates.

W = Graph number = A 

X = column number = B  + 1

Y = row number = C + 1

Z = Page number = D + 1

Example (23.00940  W = 23  X = 3 Y = 95  Z = 2)

  With this map you can now build two infinite sets of graphs

that each have infinite pages with infinite rows and columns!

They contain every rational decimal number! 

This is proof that to increase the size of infinity you must multiple by infinity!

example of work for the equation

54.650006500

Graph# = whole number

Column# = # of zeros after the . before a nonzero # +1

Row# = nonzero #s after the zero(s) that start at the .  +1

Page# = # of zeros at the end of the # +1

Graph # =54

Column # = 1

Row# =6500066

Page# =3

Example

Graph number 0  Page number 1

0.0   0.00   0.000   0.0000   0.00000   ...

0.1   0.01   0.001   0.0001   0.00001   ...

0.2   0.02   0.002   0.0002   0.00002   ...

0.3   0.03   0.003   0.0003   0.00003   ...

0.4   0.04   0.004   0.0004   0.00004   ...

...     ...       ...          ...            ...              ...

Graph number 0 Page number 2

0.00   0.000   0.0000   0.00000  0.000000   ...

0.10   0.010   0.0010   0.00010  0.000010   ...

0.20   0.020   0.0020   0.00020  0.000020   ...

0.30   0.030   0.0030   0.00030  0.000030   ...

0.40   0.040   0.0040   0.00040  0.000040   ...

...       ...          ...            ...              ...                ...

Graph number 1 Page number 1

1.0   1.00   1.000   1.0000   1.00000   ...

1.1   1.01   1.001   1.0001   1.00001   ...

1.2   1.02   1.002   1.0002   1.00002   ...

1.3   1.03   1.003   1.0003   1.00003   ...

1.4   1.04   1.004   1.0004   1.00004   ...

...     ...        ...         ...            ...              ...

This is the set of graphs

Finished 8/22/2021

  Proven and created by Ted William Griffin.