Infinity Part yx of ∞


Operation Disclosure | By Grant Ouellette, Contributing Writer

Submitted on September 22, 2021

Continued from Infinity Part y of ∞

Links to Parts x and y

Opening image: The Endless Staircase (Escher, Penrose)

Quick Recap

Part x: Georg Cantor showed that you can count through the odd numbers, the even numbers, and the counting numbers (positive integers) to the same infinity, and therefore

Infinity + Infinity = Infinity.

Part y: Cantor’s derivation of the counting numbers uses sets:

0 symbol J the empty set

1           {J} the set containing one set (the empty set)

2   {J, {J}} the set containing two sets (the empty set and the set containing the empty set)  

3 {J, {J}, {J, {J}}}the set containing three sets (the empty set, the set containing the empty set, and the set that contains the empty set and the set containing the empty set

Cantor died in 1918 so his published work is public domain.

Here’s an adapt-a-tad version of Prism’s 1980 hard rock song from the album of the same name (songwriters: J. Hall, L. Mitchell):

See Forever Eyes

Looking right through you she knows who you are she’s got see forever eyes

A spirit obsessed, a vision possessed with universal inner sight

Soaring above always searching for love the soul within her flies

Her crystal excites so follow the light of her see forever eyes

See Forever Eyes

See Forever Eyes

Beholding the mirror her eyes give a feeling of lonely vacant skies

Her crystal excites so follow the light of her see forever eyes

Soaring above always searching for love the soul within her flies

Compelling you nearer, dispelling your fear with her see forever eyes

See Forever Eyes

See Forever Eyes

Back to Brian Clegg’s book ‘A Brief History of Infinity’ the last third:

Chapter 12 to Chapter 18 (end)

Cantor dives into infinity and records his version of rules and observations.

Observation: for whole or counting numbers there is a one-to-one correspondence between each member of that set and the set of squares of those numbers; they can be paired off to infinity with the function f(x) = x times x as follows:

1 with 1, 2 with 4, 3 with 9, 4 with 16 … demonstrating there are the same number of members to each infinite set.

However, the going the other direction with the function f(x times x) = x leads to irrational number solutions, not whole numbers, for example the positive square root of 2 is 1.414 … apparently non-repeating to infinity. So there are some members of the set of squares (numbers, not humans) that are not paired off with members of the counting numbers.

Cantor takes a quantum leap away and ‘proves’ there are different levels of infinities; some infinite sets have more members than other infinite sets.

Much of this section of the book is deep thinking, advancing the above line of thought.

The continuum hypothesis is discussed: whether or not the infinity of the number line from 0 to 1 is the one true infinity.

Humans do not have the capability to understand infinity.

I see a caution issued in the title to Clegg’s Chapter 15 ‘Madness and Sanity’.

Grant’s Ideas

Rational numbers are those that can be expressed by dividing an integer by a non-zero integer, for example 1/2.

To count the infinity of rational numbers Cantor imagined a number square with infinite columns and infinite rows and demonstrated a path that ran through each number in the square (matrix). The top left to bottom right diagonal of one of Cantor’s squares gives the values 1/1 then 2/2 then 3/3 … which all reduce to 1, yet, there is this duplication and it has different meanings as visually a full pie looks different than a full pie sliced in half.

However, it appears Cantor went back to a single column with infinite rows and worked from that viewpoint to arrive at many of his infinities, different levels of infinity.

I do not see why he abandoned an infinite number of columns; it worked for him. It’s like going from 3D to 2D and expecting to see, sense or understand better.

Further, the book puts forth an argument that you can scramble Cantor’s infinite list and perform his ‘tricky’ method of showing that not all numbers are included in the 0 to 1 number line continuum – a method based on magnitude (like the counting numbers or the number line increasing to the right). So you can scramble the number list, ignoring magnitude, then apply a magnitude next-number creation ‘function’ to the list – seems perfectly logical.

I believe there is the One, the One and Infinite Creator, which can be somehow be equated to the number 1.

Everything else is a fraction (fractal) of the One; and all those fractions are on the number line, the continuum, between 0 and 1.

So I attempted to show just that.

The Cardinal Set is another name for the counting numbers. Cardinality refers to the number of members in a set.

Here is my contribution which uses infinite columns and (base) ten rows and maps each counting number to a unique decimal (based) equivalent by simply mirroring the digits of the counting number across the decimal point.

Infinite Set Comparison
1 to 1 Correspondence of the Whole or Counting Numbers to All Numbers from 0 to 1.By Grant Ouellette
Do the Whole #’s and All Numbers Between 0 and 1 have the same cardinality?February 18, 2015.
This demonstration is by the 1 to 1 mapping of each whole # to its mirror image across the decimal point;
or read each whole # from right to left including the normally omitted decimal point.
100.01     >1000.0011100.011     >9900.09910000.0001     >>
10.1110.11     >1010.1011110.111     >9910.19910010.1001     >>
20.2120.21     >1020.2011120.211     >9920.29910020.2001     >>
30.3130.31     >1030.3011130.311     >9930.39910030.3001     >>
40.4140.41     >1040.4011140.411     >9940.49910040.4001     >>
50.5150.51     >1050.5011150.511     >9950.59910050.5001     >>
60.6160.61     >1060.6011160.611     >9960.69910060.6001     >>
70.7170.71     >1070.7011170.711     >9970.79910070.7001     >>
80.8180.81     >1080.8011180.811     >9980.89910080.8001     >>
90.9190.91     >1090.9011190.911     >9990.99910090.9001     >>
In Georg Cantor’s work showing a different cardinality, he seems to assume the impossible: that there can be
a list of numbers between 0 and 1 such that there is a next number just greater than the previous one on the
list; but there is an infinite number of numbers between any 2 chosen numbers in the 0 to 1 range, so there
is no next number and therefore no possible comparison of a chosen number to the next one on the list.

Note that the simple fraction 1/3 has a decimal equivalent of 0.333 … with the 3 repeating forever and therefore only appears on my infinite matrix at infinity on the 4 th row (an infinite number of 3’s) – yet, using a base 12 number system 1/3 (presuming the same symbols for current single digit numbers) would be 0.4 which would be like magic mapped to the number 4. (Now expand to an infinite number of bases and matrices … yeehaaaa!)

Another idea: redo the recap statement for Part y above by replacing the null set symbol with the infinity symbol ∞.

This gives 3 to be the set containing 3 sets (the infinite set, the set containing the infinite set, and the set that contains the infinite set and the set that contains the infinite set) – and you can see why Cantor went bananas.

The nesting idea, like onion layers or Russian nesting dolls, can be applied to perhaps everything, including infinite possibilities and maybe even to quantum physics.

In Chapter 15 Clegg lists the 8 mathematical axioms of set theory.

The book ends with other interesting ideas.

From Here to Eternity is a 1953 American drama romance war film directed by Fred Zinneman, and written by Daniel Taradash based on the novel of the same name by James Jones. The picture deals with the US soldiers in Hawaii months before the attack on Pearl Harbor. The film won eight Academy Awards including awards for Best Picture, Best Director, Supporting Actor (Frank Sinatra), and Supporting Actress (Donna Reed). The film’s title originates from Rudyard Kipling’s 1892 poem ” Gentlemen-Rankers “, about soldiers of the British Empire who had “lost [their] way“ and were ”damned from here to eternity”. (adapted from Wikipedia)

Math Humor

Drum roll

If you wanna be healthy, natural, like e, the natural base in calculus, then remember

Euler’s Formula: eπi = – 1

It is a message about getting intoxicated: e to the pie-eyed equals minus one.


A World without Superlatives

There are no absolutes

Michael Tsarion’s book ‘The Irish Origins of Civilization’ tells of the Druids love for all life; and how they dealt with the same ancient dilemma that we face today: What do we do with a human who is lost to the darkness and incapable of rehabilitation, and will not stop murdering, and committing crimes against humanity?

The Druids kept such a person prisoner, alive for five years, and then used a tree and a rope.

Part of the dilemma is weighing the arguments ‘no living thing should be caged’ against ‘killing it’.

Harsh to some, but some might say one lifetime is minor compared to the immortal soul.

Recently there were meditations to send souls for recycling in the Galactic Sun – that’s major.

I touched on this topic before in my article ‘Mercy Per Se’


The above is evidence supporting the assertion that Source is Infinite, for if lives and souls do not have possibilities to fall to the darkness, then Source is limited. (Here Source is the set of all sets, finite and infinite sets.)

“A robin redbreast in a cage

Put all Heaven in a rage”

William Blake

Ancient Aliens episode ‘They Came from the Sea’ originally aired 28-06-2019

Caption: Examining if the oceans are acting as a giant petri dish for alien genetic experimentation

“The immortal jellyfish, when conditions become adverse, maybe temperatures become too high or salinity changes, these animals revert to a juvenile stage from the adult stage and basically start life all over again – keeps rewinding its development. In a lab there are some lines of the immortal jellyfish that haven’t experienced death yet. A jellyfish has the potential to live forever.”

In the movie Escape from Planet of the Apes there is a discussion of infinite regression based on nesting:

Here’s a painting of a landscape. The artist who painted it says: Something is missing. What is it? It is I, myself who was part of the landscape I painted. So he mentally takes a step backwards, or regresses, and paints a picture of the artist painting a picture of the landscape. But, still something is missing, and that something is still his real self painting the second picture. So he regresses further and paints a third: a picture of the artist painting a picture of the artist painting a picture of the landscape. But because something is still missing he paints fourth and a fifth until …

Infinite regression is the moment when our artist has regressed to the point of infinity and he himself becomes part of the landscape he painted (is painting) and is both the observer and the observed.

Zoo Closed Forever

Look into the future

What do you see?

A sign at the locked front gate

‘Sorry we don’t have a key’

Zoo closed forever

We let the animals go free

Zoo closed forever

They are part of our Earth family

Look into the jungle

What do you see?

A mountain gorilla reunion

The mandrill and the chimpanzee

Zoo closed forever

Let the animals run free

Zoo closed forever

Monkeys swinging tree to tree

Look into the ocean

What do you see?

A world infused with harmony

All living things swimming free

Zoo closed forever

Let the octopi just be

Zoo closed forever

Let the fish swim the sea

Look into the sweet air

What do you see?

A butterfly and a honeybee

Birds circling, gliding, flying free

Zoo closed forever

Let the reptiles and the insects be

Zoo closed forever

Let the amphibians be free

Zoo closed forever

Let the animals go free

Zoo closed forever

We are Mother Nature’s family

Affirmation: I Am the Resurrection and the Light of the Ascended Cosmic Christ Peace – the Peace that surpasses the lower limited mind – the Peace that I had with God in the beginning before the world was – eternally sustained and ever expanding.


In Timelessness You Live And Breathe And You Will Enter A New Phase Of Expansion And You Will Become The Travelers To The Earth You Left.

The opening lines to Burton Cummings’ 1976 song Timeless Love:

Timeless love is livin’ on

Here in my heart baby

And here in my song


What is eternal, remains, what is not, disappears.

For example, God remains, Niburu has disappeared.

Kryon through Lee Carroll: You can do anything, not everything.

Barbara Marciniak’s Bringers of the Dawn:

Dimensions are densities of light. There are an infinite number of dimensions in the octave format.

Link to Elvis’s Glory, Glory, Hallelujah video

Glory, Glory, Hallelujah

His Truth is marching on

His Truth is marching on


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