Copyright 2016-2023 by Louis Epstein,All Rights Reserved

A power-tower of a
Zurvanic Absolute Number
POPBLED
the Zurvanic Absolute Number
popbled
the Zurvanic Absolute Number
times,
times

Zurvanic Absolute Numbers,

each surrounded by Moser polygons of a number equal to

the Zurvanic Absolute Number times the Zurvanic Absolute Number power of
its upward-counting ordinal as every term in a
Zurvanic-Absolute-Number-per-dimension,
Zurvanic Absolute Number dimensional Bowers array,

each polygon having a number of sides equal to
the number of Zurvanic Absolute Numbers,raised to itself
the-Zurvanic-Absolute-Number-popbled Zurvanic Absolute Numbers
of times,
popbled a number of times equal to
the Zurvanic Absolute Number in a
Zurvanic-Absolute-Number-in-a-Zurvanic-Absolute-Number-gon-gon
times
a power tower of the number of polygons surrounding that particular
Zurvanic Absolute Number
raised to
the Zurvanic Absolute Number times its Zurvanic Absolute Number power
in a number of layers equal to
the Zurvanic Absolute Number times the Zurvanic Absolute Number power of
the Zurvanic Absolute Number
times
itself-raised-to-the-Zurvanic-Absolute-Number-times-its-Zurvanic-Absolute-Number-in-a-Zurvanic-Absolute-Number-gon-power,

the whole popbled
the Zurvanic Absolute Number
times
the number of times expressed by a chain of Conway arrows between
every number rising from twenty-nine to the
Zurvanic Absolute Number power of the Zurvanic Absolute Number power of
the Zurvanic Absolute Number,
plus
the Zurvanic Absolute Number
ultrexed
the Zurvanic Absolute Number of
times to the Zurvanic Absolute Number,
each number repeated
the Zurvanic Absolute Number of times,

is defined as "the Number **a**",
first of *The Alphabet Numbers*.

The convoluted collection of operations described above is *the Alphabet
Number function*.

Perform the Alphabet Number Function on The Number **a**
(substituted in each instance for the Zurvanic Absolute Number) and
repeat **a** times,and you reach the Number **A**,perform it on
**A** repeating **A** times and you reach The Number **b**,
and so on through the alphabet.

Performing the function on the Number **Z** that many times yields
the Number **aa**,followed in sequence by **aA**,**ab**,and
so forth...after **aZ** comes **Aa**,after **ZZ** comes
**aaa**,and so on.

In this terminology,we quickly realize that
**TWO** plus
**TWO** is a lot less than **FOUR**,
which is more than **SIX** but much less than **ZERO**,while
every number discussed so far is a great deal less than
**NOTHING**.

We also discover that **SOMETHING** is much greater than
**INFINITY** even though it doesn't come close to
**CHUMPCHANGE**.What's more,**BIGGERTHANINFINITY**
is way less than **MUCHTOOSMALLTOMENTION**.

And we realize that we need even more methods of conveying numbers much
larger.

{

and that expressed by THAT many Zs is

{

while the number expressed by repeating the single-colon-separated Zs

{

.

The number expressed by THAT many **Z**s is

{**Z**:**Z**::**Z**}

while the number expressed by using **that many colons** to separate
**Z**s is

{**Z**[**Z**::**Z**]**Z**}

Alphabet Numbers separated by N colons convert to

{(first alphabet number)((N-1 colons,second alphabet number -1) repeated
second alphabet number -1 times)}

To convey using **that many layers of square brackets** use

{**Z**{[**Z**::**Z**]**Z**}}.

Brackets resolve from inside to out and right to left.

{**ONE**:**TWO**:**THREE**:**FOUR**}

means **FOUR** repetitions of **THREE** is the number of repetitions
of **TWO** needed to express the number of repetitions of **ONE** to
express the intended number,while

{**ONE**[**TWO**:**THREE**]**FOUR**}

means **THREE** repetitions of **TWO** is the number of colons
to calculate with in repeating **FOUR** repetitions of **FOUR**
(working leftward and repeating **FOUR** each successively calculated
number of times) to get the number of repetitions of **ONE**.

The rightmost bracket closes all unclosed pairs,if any are outstanding.

The Number

{**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE**

(**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE** colons)

{[**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE**

(**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE** colons)

{[**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE**

(**GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE** colons)

.

.

.

(repeated **GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE!** layers)

.

.

.

**ISAIDGREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE!**}

**Z**s express *Epstein's First Number*,or E_{(1)}...
in full "E_{(1,0,0,0,0...)}" as explained hereafter.

1.Popble E_{(n)} E_{(n)} times.

2.Perform the Alphabet Number Function on the number resulting
from Step 1,that many times.

3.The Number expressed by *the number resulting from Step 2
Zs* is then substituted for

4.Steps 1-3 are repeated E

E(E(E(E(E(...E(n) layers...(n))))))

is also E_{(n,1)}.

E(E(E(E(E(...E(n,1) layers...(n,1))))))

is also E_{(n,2)}.

E(E(E(E(E(...E(E(n),E(n)layers) layers...(E(n),E(n)))))))

is also E_{(n,1,1)}.

E(E(E(E(E(...E(E(E(n),E(n),E(n)),(E(n),E(n),E(n) layers)layers)
layers...(E(n),E(n),E(n))))))))

is also E_{(n,1,1,1)}.

etc.

E

Of course that's so easily beatable...

the Second Nominated Number with

the Number expressed by

the Second Nominated Number,with the Alphabet Number function performed
upon it

the number of times expressed by a chain of Conway arrows
between ten repetitions of every number from five to itself ultrexed twice
to its factorial,

**Z**s
repetitions

of this number of repetitions

interpolated after the
first "THIS",and E_{(that number of repetitions)} repetitions
of *that* number interpolated after the first "NUMBER",and
the number of layers of E-subscripting before the immediately
preceding number is used to to get the number and its
number of repetitions raised to itself in a power-tower of
the immediately preceding number of times after every succeeding
array generation(Alphabet Number in the specification).

This is the embryo of the * Epstein Number Nominating
Function*.

From this point,to get from Unofficially Nominated Number n to Unofficially Nominated Number n+1,a similar interpolation of additional generations is performed as follows.

1.After the first specified generation in EUNN n,

add the Alphabet Number described by

EUNN n with the Alphabet Number Function performed upon it

E_{(1,2,3,...E(EUNN n))} times,

**Z**'s,

repetitions of that Alphabet Number.

2.After each succeeding generation,interpolate

E_{E(...number of layers of subscripting equal to number interpolated
after preceding generation raised to itself in a power tower of a number
of layers equal to itself)(number interpolated in previous
generation))}) repetitions of this new number of
repetitions.

3.Repeat steps 1 and 2,substituting the entire number achieved
after step 2 for EUNN n in step 1,

E_{(1,2,3,4,...E(E(EUNN n layers of subscripting)(EUNN
n)))} times.

When EUNN n reaches E_{(1,2,3,...EE(Epstein's Third
Unofficially Nominated number of layers of subscripts)(Epstein's Third
Unofficially Nominated Number)))} we have reached
*Epstein's One Step Toward A Little Bit Seriously Nominated
Number*.

The increment in EUNN n to take ESTALBSNN n to n + 1 is the

E_{(1,1,2,2,3,3...EE(ESTALBSNN n layers of
subscripts)(ESTALBSNN
n,repeated ESTALBSNN n times))) }
power of the previous number.

When ESTALBSNN n reaches E_{((every integer
from 1 repeated twice its square times)...E(E(EEpstein's
Fourth Step Toward A Little Bit Seriously Nominated Number)
layers of subscripts)(Epstein's Fourth Step Toward a Little Bit Seriously
Nominated Number,repeated E(Epstein's Fourth Step Toward a Little Bit
Seriously Nominated Number) times)))} we have reached
*Epstein's First A Little Bit Seriously Nominated Number*.

The increment in ESTALBSNN n to take EALBSNN n to n+1 is
a power tower
of the previous increment raised to
E_{((every integer from 1 repeated thrice its cube times)...E(E(EALBSNN
n,repeated E(EALBSNN n layers of subscripts) layers of
subscripts)(EALBSNN n),
repeated that many times)))}) that many times.

When EALBSNN n reaches E_{((every integer
from 1 repeated four times its fourth power
times)...E(E(EEpstein's
Fifth A Little Bit Seriously Nominated Number,repeated
Epstein's Fifth A Little Bit Seriously Nominated Number times
) layers of subscripts)(E(Epstein's Fifth A Little Bit Seriously
Nominated Number,repeated Epstein's Fifth A Little Bit Seriously Nominated
Number times),repeated E(Epstein's Fifth A Little Bit
Seriously Nominated Number) times)))} we have reached
*Epstein's First Step Toward Semi-Seriously Nominated Number*.

The increment in EALBSNN n to take ESTSSNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated four times its fifth power
times)...E(E(ESTSSNN
n,repeated E(E(ESTSSNN n,repeated ESTSSNN n times) layers of subscripts)
layers of subscripts)(ESTSSNN n),
repeated that many times)))) that many times)} raised to
itself that many times.

When ESTSSNN n reaches E_{E((every integer
from 1 repeated four times its sixth power
times)...E(E(E(Epstein's
Sixth Step Toward Semi-Seriously Nominated Number,repeated
E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number) times
) layers of subscripts)(E(Epstein's Sixth Step Toward Semi-Seriously
Nominated Number,repeated E(Epstein's Sixth Step Toward Semi-Seriously
Nominated Number) times),repeated E(Epstein's Sixth Step Toward
Semi-Seriously Nominated Number) times))))}
we have reached
*Epstein's First Semi-Seriously Nominated Number*.

The increment in ESTSSNN n to take ESSNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated four times its seventh power
times)...E(E(ESSNN n,repeated E(E(ESSNN n,repeated E(E(ESSNN
n,repeated ESSNN n times) times) layers of subscripts)
layers of subscripts)(E(ESSNN n,repeated ESSNN n times)),
repeated that many times)))) that many times)} raised to
itself E(that many times) times.

When ESSNN n reaches E_{E((every integer
from 1 repeated four times its eighth power
times)...E(E(E(Epstein's
Seventh Semi-Seriously Nominated Number,repeated
E(Epstein's Seventh Semi-Seriously Nominated Number) times
) layers of subscripts)(E(Epstein's Seventh Semi-Seriously
Nominated Number,repeated E(Epstein's Seventh Semi-Seriously
Nominated Number) times),repeated E(Epstein's Seventh
Semi-Seriously Nominated Number)
times))),repeated E(that many times) times)}
we have reached
*Epstein's First Step Toward Almost Seriously Nominated Number*.

The increment in ESSNN n to take ESTASNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated four times its ninth power
times)...E(E(ESTASNN n,repeated E(E(ESTASNN n,repeated E(E(ESTASNN
n,repeated E(ESTASNN n,repeated ESTASNN n times) times) times) layers of
subscripts)
layers of subscripts)(E(ESTASNN n,repeated E(ESTASNN n) times)),
repeated that many times)))) that many times)} raised to
itself E(that many times,repeated E_{(that many times)} times)
times.

When ESTASNN n reaches E_{E((every integer
from 1 repeated five times its tenth power
times)...E(E(E(Epstein's
Eighth Step Toward Almost Seriously Nominated Number,repeated
E(Epstein's Eighth Step Toward AlmostSeriously Nominated Number) times
) layers of subscripts)(E(Epstein's Eighth Step Toward
Almost Seriously Nominated Number,repeated E(Epstein's Eighth
Step Toward Almost Seriously Nominated Number) times),repeated E
(Epstein's Eighth Step Toward Almost Seriously Nominated Number,
repeated E(Epstein's Eighth Step Toward Almost Seriously Nominated
Number) times)
times))),repeated E(that many times,repeated E(that many
times)times ) times)}
we have reached
*Epstein's First Almost Seriously Nominated Number*.

The increment in ESTASNN n to take EASNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated six times its twelfth power
times)...E(E(EASNN n,repeated E(E(EASNN n,repeated E(E(EASNN
n,repeated E(EASNN n,repeated E(EASNNN n,repeated EASNN n times) times)
times) times) layers of
subscripts)
layers of subscripts)(E(EASNN n,repeated E(EASNN n,repeated EASNN n times)
times)),
repeated that many times)))) that many times)} raised to
itself E(that many times,repeated E(E_{(that many times)}) times)
times.

When EASNN n reaches E_{E((every integer
from 1 repeated ten times its twentieth power
times)...E(E(E(Epstein's
Ninth Almost Seriously Nominated Number,repeated
E(Epstein's Ninth Almost Seriously Nominated Number,repeated
E(Epstein's Ninth Almost Seriously Nominated Number) times) times
) layers of subscripts)(E(Epstein's Ninth
Almost Seriously Nominated Number,repeated E(Epstein's Ninth
Almost Seriously Nominated Number) times),repeated E
(Epstein's Ninth Almost Seriously Nominated Number,
repeated E(Epstein's Ninth Almost Seriously Nominated
Number) times)
times))),repeated E(that many times,repeated E(that many
times)times ) times)}
we have reached
*Epstein's First Step Toward Seriously Nominated Number*.

The increment in EASNN n to take ESTSNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated ten times its twenty-fifth power
popbled times)...E(E(ESTSNN n,repeated E(E(ESTSNN n,repeated E(E(ESTSNN
n,repeated E(ESTSNN n,repeated E(ESTSNN n,repeated E(ESTSNN n) times)
times)
times) times) layers of subscripts)
layers of subscripts)(E(ESTSNN n,repeated E(ESTSNN n,repeated E(ESTSNN n)
times) times)),
repeated that many times)))) that many times)} raised to
itself E(E_{(that many times)},repeated E(E_{(E(that many
times))}) times)
times.

When ESTSNN n reaches E_{E((every integer
from 1 repeated twenty times its thirtieth power popbled
times)...E(E(E(Epstein's
Tenth Step Toward Seriously Nominated Number,repeated
E(Epstein's Tenth Step Toward Seriously Nominated Number,repeated
E(Epstein's Tenth Step Toward Seriously Nominated Number) times) times
) layers of subscripts)(E(Epstein's Tenth Step
Toward Seriously Nominated Number,repeated E(Epstein's Tenth Step
Toward Seriously Nominated Number) times),repeated E
(Epstein's Tenth Step Toward Seriously Nominated Number,
repeated E(Epstein's Tenth Step Toward Seriously Nominated
Number,repeated E(Epstein's Tenth Step Toward Seriously Nominated
Number) times) times)
times))),repeated E(that many times,repeated E(that many
times)times ) times)}
we have at last reached
*Epstein's First Seriously Nominated Number*.

The increment in ESTSNN n to take ESNN n to n + 1 is
a power tower
of E_{(the previous increment raised to
E((every integer from 1 repeated twenty-two times its fortieth
power,popbled twice,times)...E(E(ESNN n,repeated E(E(ESNN n,repeated
E(E(ESNN
n,repeated E(ESNN n,repeated E(E(ESNN n),repeated E(ESNN n) times)
times)
times) times) layers of subscripts)
layers of subscripts)(E(E(ESNN n),repeated E(ESNN n,repeated E(ESNN
n,repreated ESNN n times))
times) times)),
repeated that many times)))) that many times)} raised to
itself E(E_{(that many times)},repeated E(E_{(E(that many
times))}) times)
times.

The one expressed by the

E_{((every integer starting with 1,repeated E(E(nn... in a
power tower of nn layers) layers of subscripts)(nn...
in a power tower of nn layers)) times...to the
last repetition of E(E(Epstein's First Seriously Nominated
Number layers of subscripts)(Epstein's First Seriously Nominated Number,
repeated E(Epstein's First Seriously Nominated Number) times))
)}

Seriously Nominated Number of

**Z**'s,

all bracketed and individually separated by like number of
colons in each instance.

E_{(E(E(...(E(Transitional Nominee,repeated E(Transitional Nominee)
times) layers of subscripts)...(E(1),E(1,1),etc until we reach
E(every integer starting with 1,repeated E(E(nn... in a
power tower of nn... in a power tower of
E(nn,repeated E(Transitional Nominee) times) layers)
layers of subscripts)(nn...
in a power tower of E(nn) layers)) times...to the
last repetition of E(E(E(Transitional Nominee)
layers of subscripts)(E(Transitional Nominee),
repeated E(Transitional Nominee,repeated E(Transitional Nominee)
times)))
}

is *Epstein's First Really Seriously Nominated Number*,or
**E ^{1}R_{1}SNN.**

To increment **E ^{1}R_{n}SNN** to

(E

When **n** of **E ^{1}R_{n}SNN** reaches

Hereafter,**E ^{n}R_{E(E(EnRE(n)SNN)
layers of subscripts)((EnRE(n)SNN,repeated
E(EnRE(n,n)SNN) times))}SNN
= E^{n+1}R_{1}SNN.**

The formula for incrementing the subscripted R-number
in succeeding generations of the superscripted-prefixed R number
is modified by requiring that the substitution of the expanded
formula for each occurrence of the subscripted number
take place not once,but **E ^{n}R_{1}SNN times.**

Of course *n* in ^{n}R is like the number of an Epstein
number just shorthand for (*n*,0,0,0,0...).

Thus,

E^{E(E(E(E(E(...E(n)
layers...(EnR1SNN))))))}R_{1}SNN

is also E^{(n,1)}R_{1}SNN.

E^{E(E(E(E(E(...E(n,1)
layers...(E(n,1)R1SNN)))))}R_{1}SNN

is also E^{(n,2)}R_{1}SNN.

E^{E(E(E(E(E(...E(E(n),E(n)layers)
layers...(E(E(n,n)R1SNN),
E(E(n,n)R1SNN))))))))}R_{1}SNN

is also E^{(n,1,1)}R_{1}SNN.

E^{E(E(E(E(E(...E(E(E(n),E(n),E(n)),(E(n),E(n),E(n) layers)layers)
layers...(E(E(n,n,n)R1SNN),
(E(n,n,n)R1SNN),(E(n,n,n)R1SNN)))))))))
}R_{1}SNN

is also E^{(n,1,1,1)}R_{1}SNN.

etc.

Armed with this escalation formula,we proceed to define the

The preceding superscript of R has as its comma-separated generations
every integer starting with 1,repeated
E(E^{
(every integer from 1 to
E(E9R9SNN)R9SNN)}R_{9}SNN)
raised to itself in a power
tower of E^{
(every integer from 1 to EE9R9SNN
R9SNN) layers,times,to the
last repetition of
E(E(E(E(9,9)RE(9)SNN))layers of
subscripts)
(E(E9R9SNN),
repeated E((E9R9SNN),repeated
E(E(E9R9SNN)times))times)))
The subscript is E(9,9,9)RE(9,9,9)SNN.
And the First Kingmaker Number is that many Zs
individually separated by as many colons within a set of brackets.
}

1.Every integer from 1 to E

2.

Then every possible sequence of

Then every possible sequence of

3.After the last repetition of the entire sequence of integers, repeat steps 1 and 2 working out of the set of integers between 2 and the Terminal Number,with the number of layers of subscripts, and of the repetitions of each E(number) or E(sequence) in defining the number of repetitions,raised to a power tower with the Kingmaker Number as the base,followed by E(n)(or E(sequence)) layers of E(n) (or E(sequence)) followed by a number of ascending layers of First Kingmaker Numbers defined by the value of the E-layers.

4.Repeat step 3 with the set of integers between 3 and the Terminal
Number,then the set between 4 and the Terminal Number,etc.

5.Repeat steps 1-4 E(First Kingmaker Number) times,with the number of
subscripts/repetitions never resetting but continuing to be exponentiated
throughout.

The subscript of this number is E(First Kingmaker Number repetitions of Terminal Number).

Since I was implored by a reader who stayed up until 1 AM reading the previous nomination to keep going...

is

E_{E(E...E(EEnSNN,repeated E(EEnSNN,repeated...
(E(EEnSNN,repeated E(EEnSNN)times repetitions of
this)...times)times) layers of subscripts)
E(EEnSNN,repeated E (EEnSNN,repeated E(EEnSNN,
repeated... (E(EEnSNN,repeated E(EEnSNN)times repetitions of
this)...times)times) layers of subscripts...(E(E(E(EEnSNN)))
times)}
= EE_{n+1}SNN.

When **n** reaches E(the following sequence:)

1.Every integer from 1 to
E(E(EE_{1}SNN^{EE2SNN...(power tower rising to
EEEE999SNNSNN)}) repetitions of every number
from 1 to E(E(EE_{{REALLY::BIG::ALPHABET::NUMBER}}SNN,repeated
E(EE_{{AN::EVEN::BIGGER::ALPHABET::NUMBER}}SNN times)
))SNN,
each number repeated (E(EE_{n}SNN) layers of subscripts)
(E(E(EE_{n}SNN) repeated E((EE_{n}SNN)
times)).
We shall call the designated maximum number here the
*first terminal number* of this specification.

2.*Every possible sequence of any two integers,duplication permitted*
between 1 and the terminal number...each sequence ordered in ascending
order of Epstein Number value potential,each repeated (E(the sequence)
layers of subscripts)(E(E(the sequence) repeated E(the sequence)
times)).

Then every possible sequence of *three* integers between 1 and the
terminal number,likewise.(always no limit on duplicate numbers)

Then every possible sequence of *four* integers between 1 and the
terminal number,likewise...et cetera.

3.After the last repetition of the entire sequence of integers,
repeat steps 1 and 2 working out of the set of integers between
2 and the terminal number,with the number of layers of subscripts,
and of the repetitions of each E(number) or E(sequence) in defining
the number of repetitions,raised to a power tower with the terminal
number as the base,followed by E(E(n))(or E(E)sequence))) layers of
E(E(n)) (or E(E(sequence))) followed by a number of ascending layers of
EE_{n counting up from 1}SNN numbers
defined by the value of the E-layers.

4.Repeat step 3 with the set of integers between 3 and the terminal
number,then the set between 4 and the terminal number,etc.

5.Repeat steps 1-4 E(first terminal number) times,with the number of
subscripts/repetitions never resetting but continuing to be exponentiated
throughout.

6.Repeat steps 1-5 E(E...(E(first terminal number) layers of subscripts)
(E(first terminal number),repeated E(first terminal number) times) times,
**substituting the number of repetitions used for the final sequence
of numbers in the last cycle of step 5 for the first terminal number**.

we have reached **Epstein's First Extra Extraordinarily Seriously
Nominated Number**,or **EE _{1}ESNN**,which starts a new
generation.

Incrementing EE_{n}ESNN uses the formula used for incrementing
EE_{n}SNN except that EE_{n}ESNN is substituted for
EE_{n}SNN on every occasion and in the specifications of the
numbers of layers of subscripts and of the repetitions,this substitution
of the full number of subscripts and repetitions for the specified
number is then repeated EE_{n}ESNN times.

When this latest **n** reaches E(the following sequence:)

1.Every integer from 1 to
E(E(EE_{1}ESNN^{EE2ESNN...(power tower rising to
EEEE(999 layers of subscripts)
EE999ESNNESNNESNN)})
repetitions of every number
from 1 to
E(E(EE_{EE...E(999) layers of
subscripts...EE(999)ESNNESNN,repeated
E(EEE
E({AN::EVEN::LARGER::ALPHABET::NUMBER}) layers of
subscripts...EE(99999)ESNN
ESNN times)
))}ESNN,
each number repeated (E(EE_{n}ESNN) layers of subscripts)
(E(E(EE_{n}ESNN) repeated E((EE_{n}ESNN)
times)).
We again call the designated maximum number here the
*first terminal number* of this specification.

2.*Every possible sequence of any two integers,duplication permitted*
between 1 and the terminal number...each sequence ordered in ascending
order of Epstein Number value potential,each repeated (E(
EE_{(the sequence)}ESNN)
layers of subscripts)(E(E(EE_{(the sequence)}ESNN) repeated
E(EE_{(the sequence)}ESNN times)).

Then every possible sequence of *three* integers between 1 and the
terminal number,likewise.(always no limit on duplicate numbers)

Then every possible sequence of *four* integers between 1 and the
terminal number,likewise...et cetera.

3.After the last repetition of the entire sequence of integers,
repeat steps 1 and 2 working out of the set of integers between
2 and the terminal number,with the number of layers of subscripts,
and of the repetitions of each E(number) or E(sequence) in defining
the number of repetitions,raised to a power tower with the terminal
number as the base,followed by E(E(EE_{n}ESNN))
(or E(E(EE_{sequence}ESNN)))
layers of
E(E(EE_{n}ESNN)) (or E(E(EE_{sequence}ESNN))) followed by
a number of ascending layers of
EE_{n counting up from 1}ESNN numbers
defined by the value of the E-layers.

4.Repeat step 3 with the set of integers between 3 and the terminal
number,then the set between 4 and the terminal number,etc.

5.Repeat steps 1-4 E(first terminal number) times,with the number of
subscripts/repetitions never resetting but continuing to be exponentiated
throughout.

6.Repeat steps 1-5 E(E...(E(EE_{first terminal number}ESNN) layers
of subscripts)(E(EE_{first terminal number}ESNN),repeated
(EE_{(EEfirst terminal numberESNN)}ESNN layers
of subscripts)(EE_{first terminal number}ESNN,repeated
(EE_{first terminal number}ESNN)times)) times) times,
**substituting the number of repetitions used for the final sequence
of numbers in the last cycle of step 5 for the first terminal number**.

we reach another arbitary turning point number.

When we take the Alphabet Number represented by *this many Zs*
each separated by a like number of colons

Incrementing EV_{n}ESNN uses the formula used for incrementing
EE_{n}ESNN except that EV_{n}ESNN is substituted for
EE_{n}ESNN on every occasion and in the specifications of the
numbers of layers of subscripts and of the repetitions,this substitution
of the full number of subscripts and repetitions for the specified
number is then repeated EV_{(EVnESNN layers of
subscripts)(E(EVnESNN),repeated E(EVnESNN)
times)}ESNN times.

When the number of subscripts in EV_{n}ESNN
and this latest **n** reaches EV_{(the following
sequence:)}ESNN

1.Every integer from 1 to
E(E(EV_{1}ESNN^{EV2ESNN...(power tower rising to
EVEV(E(9,9,9) layers of subscripts)
EEE(9,9,9)ESNNESNNESNN)})
repetitions of every number
from 1 to
E(E(EV_{EV...E(9,9,9) layers of
subscripts...EVE(9,9,9)ESNNESNN,repeated
E(EVE
E({AN::ENORMOUSLY::LARGER::ALPHABET::NUMBER}) layers of
subscripts...EVE(9,9,9,9,9)ESNN
ESNN times)
))}ESNN,
each number repeated (E(EV_{n}ESNN) layers of subscripts)
(E(E(EV_{n}ESNN) repeated E((EV_{n}ESNN)
times))times.
We again call the designated maximum number here the
"first terminal number" of this specification.

2.*Every possible sequence of any two integers,duplication permitted*
between 1 and the terminal number...each sequence ordered in ascending
order of Epstein Number value potential,each repeated (E(
EV_{(the sequence)}ESNN)
layers of subscripts)(E(E(EV_{(the sequence)}ESNN) repeated
E(EV_{(the sequence)}ESNN times)).

Then every possible sequence of *three* integers between 1 and the
terminal number,likewise.(always no limit on duplicate numbers)

Then every possible sequence of *four* integers between 1 and the
terminal number,likewise...et cetera.

3.After the last repetition of the entire sequence of integers,
repeat steps 1 and 2 working out of the set of integers between
2 and the terminal number,with the number of layers of subscripts,
and of the repetitions of each E(number) or E(sequence) in defining
the number of repetitions,raised to a power tower with the terminal
number as the base,followed by E(E(EV_{n}ESNN))
(or E(E(EV_{sequence}ESNN)))
layers of
E(E(EV_{n}ESNN)) (or E(E(EV_{sequence}ESNN))) followed by
a number of ascending layers of
EV_{EVn counting up from 1ESNN}ESNN numbers
defined by the value of the E-layers.

4.Repeat step 3 with the set of integers between 3 and the terminal
number,then the set between 4 and the terminal number,etc.

5.Repeat steps 1-4 EV_{(first terminal number)}ESNN times,with the
number of subscripts/repetitions never resetting but continuing to be
exponentiated throughout.

6.Repeat steps 1-5 E(E...(E(EV_{first terminal number}ESNN) layers
of subscripts)(E(EV_{first terminal number}ESNN),repeated
(E(EV_{first terminal number}ESNN)layers of subscripts)
E(EV_{first terminal number}ESNN,repeated
(EV_{E(first terminal number,repeated itself ultrexed
itself times to itself times)}ESNN)times)) times) times,
substituting the number of repetitions used for the final sequence
of numbers in the last cycle of step 5 for the first terminal number.

7.Repeat steps 1-6 EV_{(number of subscripts equal to the number of times
steps 1-5 were repeated in the previous repetition of step 6)(EVthat number,
repeated that many timesESNN,repeated itself cubed times)}ESNN
times,substituting the number of repetitions used for the
final sequence of numbers in the last cycle of step 6 for the first
terminal number.

**Steps 8-
E(E...(E(EV _{first terminal number}ESNN) layers
of subscripts)(E(EV_{first terminal number}ESNN),repeated
(E(EV_{first terminal number}ESNN)layers of subscripts)
E(EV_{first terminal number}ESNN,repeated
(EV_{E(first terminal number,repeated itself ultrexed
itself times to itself times)}ESNN)times)) times) times)**.
These steps follow the pattern laid out in Step 7,relating to Step
(Step number -1).

we reach another passing Kingmaker-Number...

The Alphabet Number expressed by that many **Z**s each separated
by colons,the first two by that many,each working rightward by the
previous number ultrexed that number of times to itself is another,
while if one uses that Alphabet Number as the first terminal number
of the specification used to generate the previous Kingmaker-Number
and then repeats this process that whole Kingmaker Number of times,
one reaches **Epstein's first Very,Very Extraordinarily Seriously
Nominated Number**,or **E ^{2}V_{1}ESNN**.

Incrementing E^{2}V_{n}ESNN uses the formula used for
incrementing
EV_{n}ESNN except that E^{2}V_{n}ESNN is
substituted for
EV_{n}ESNN on every occasion and in the specifications of the
numbers of layers of subscripts and of the repetitions,this substitution
of the full number of subscripts and repetitions for the specified
number is then repeated EV_{(E2VnESNN layers of
subscripts)(E(E2VnESNN),repeated
E(E2VnESNN,repeated
E2V(E(n,n,n))ESNN times)
times)}ESNN times.

The Alphabet Number expressed by that many

was my standard-bearing nominee as highest named calculable number when a disk crash took this page offline in April 2017.

Getting this page back up calls for

Popble the Alphabet Number with "Resurrection Celebration Number 2"
**Z**s 2020 times.
My next nominee as largest calculatable number is

(the result of that
popbling)* hu*',

So my next nominee as largest calculatable number was
the Blindingly Big Number:

(2020 Vision Number)(*s*)',_{(2020 Vision number popbled E(20,20)
times)s'}'

The day after that I realized that function was weak tea and came up
with the Ladder Hyper-Operating Transformer Function
which could enable substantially greater numbers,that would blind one to
the Blindingly Big Number for good reason...
So my NEW nominee as largest calculatable number was the Big LHOT:

(Blindingly Big Number)(*l*)',_{(Blindingly Big Number popbled
E(T,W,E,N,T,Y,T,W,E,N,T,Y) times)l'}'

(Big LHOT popbled Big LHOT times)_{{s}}→

The Alphabet Number with 2021 Contender

Popble the Restless Number
E_{(TWENTY,TWENTY,TWO)}
quettillia-ronnillia'quettillio-ronnillio-quettillion times
and call the resulting number Second Order **a**.

Place Second Order **a** in the Alphabet Number function,
performing the function that many times,to yield Second Order
**A**,and continue through *every calculation on this page*
to redefine new-order Alphabet Numbers,Epstein Numbers,and so forth,
using the new order versions in the definitions.

When you reach the Second Order Restless Number,popble it as many times
as the first was,and repeat *all* the calculations in defining new
*Third Order* Alphabet Numbers,Epstein Numbers,etc. used to define
their counterparts.

Repeat all steps before this one twice.

Repeat all steps before this one three times.

Repeat all steps before this one four times...

...and so forth until you have made the repetition cycle of producing
new order numbers that is Restless-Number-popbled-E_{(TWENTY,
TWENTY,TWO)}-quettillia-ronnillia'quettillio-ronnillio-quettillion-times
steps long...producing the latest-order reincarnation of the Restless
Number.

The 2022 Contender is the latest-order Alphabet Number with *that many Zs*
each separated by that many colons.

Perform the Alphabet Number function on the 2022 Contender E

Perform all the calculations,using this order,to turn that **a**
into the 2022 Contender of that new order.

Repeat all steps before this one twice.

Repeat all steps before this one three times.

Repeat all steps before this one four times...

...when you reach the 2022-Contender-steps-number
of repetition cycles,"reverse gear with a square"...
the next set of repetitions is 2022-Contender-minus-one
squared,then 2022-Contender minus-two-squared,and so
on down the squares until you get to a cycle of four
repetitions,then do three-cubed repetitions,four-cubed,
and so on until you get up to 2022-Contender-minus-two cubed,
then again reverse incrementing the exponent until you get
down to three to the fourth,reverse incrementing starting
with four to the fifth,up to 2022-Contender-minus-three
to the fifth,reverse using sixth powers,and so on with
just-one-short cycles reversing with higher powers until
there is no room to reverse.
At that point,create a new-order **a** and do all
the steps to reach that order's 2022 Contender,
and repeat ALL foregoing steps 2022-Contender-popbled
times.
The 2023 Contender is the latest-order Alphabet Number with *that many
Zs* each separated by 2023 times that many colons.

Prove another comparably calculable number is bigger,and I'll go further...

If this number feels too small,popble the number the-number-popbled times, and repeat until the feeling goes away...or

Keep counting...

Louis Epstein

First edition January 4,2016

Second Nominated Number added January 5,2016

HTML tweaks and Third Nominated Number added January 6,2016

Expansion to the Transitional Nominee on January 9th 2016,and new nominee,followed by Extraordinarily Serious extension, January 12th.Further nominees January 13th and 15th. Enhancement with ultrex & nominee tweaks February 4th-11th.

Correction & E

New nominee tweaks July 8th 2016 and March 4th 2017.

Resurrection Celebration September 11th 2017, second celebration on the 18th,some fixes the 21st.

Revision introducing the 2020 Vision Number April 24,2020,the Blindingly Big Number April 25,2020,and the Big LHOT April 26,2020.

Link revised for renaming of SHOT April 27,2020.

Revision introducing 2021 Contender January 4,2021.

Restless Number introduced October 2,2021,with a typo fix.

2022 Contender introduced November 28,2022

2023 Contender introduced February 11,2023,typo fixes March 21.

Do you just want a shortcut to the ultimate number? (not computable)

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