15 January 2014
Beatrix matrix system
sets number record!
by Giga Gerard
mathematical artist
A public gift of the largest natural number in mathematics, dedicated to the departing Queen Beatrix of the Netherlands, in gratitude for the prosperous period of her reign. Created for the occassion of the coronation on 30 April 2013 of her son King Willem Alexander, ruling with the lovely Máxima of Argentina on his side. „Viva la Reina!”
A deep matrix called Btrix is set up for the Big number championship against Chris Bird's Beaf algorithm. Subsequently we crown it with the mindboggling “Beatrix Máxima” with good hope the Dutch royal family will accept their new world record number, following the national festivities in the year 2013.
Big numbers are numbers without practical purpose, neither
outside
nor
inside
of mathematics.
But we can define ever larger structures
and smarter algorithms to create increasingly Big numbers.
By comparison this world is rather small,
we cannot resolve those numbers completely.
# Index
“Beatrix matrix system
sets number record!”
April 2013March 2014…
Mathemagical article by Giga Gerard on
the construction of a Royal Dutch largest number.

Start to count

Only ones
11111

Only ones

Big

Decimal numbers
1000

Scientific E
1E120

Boundary of arithmetic
10^10^100

Decimal numbers

Historical records

Archimedes octads
1E8E16

Buddhist unspeakable tower
10^^(10^(7×2^119))

Guinness Graham's number
3→3→4#64
 Bowers meameamealokkapoowa oompa
 Bird beyond nested arrays III
 Rayo afterwords

Archimedes octads

To B or not...

Structures by RepExp
F(..n..) :3: = F(F(F(n)))

Conventions
Btrix(a) = a

Choice rules
a,b, = a,b = b

Adding by abacus
a,b,1 = a,ab, = ab

Structures by RepExp

...to Be superstars

Multiply by triple
a,b,c = a*c+b
Eaf 
Powers by upload
a,b,,c = a**c+*b

Tetration
a,b,,,c = a***c+**b
Ñ_{0} 
Linear arrays
a,,{c}b = a*^{..}b *:c
Eaf

Multiply by triple

Bea's dimensions

Second row
a,b,[1]1c = a,{b}a,[1]c

On the plane
a,b.,[1]..1 :c ≈> Eaf(a,b,b,c)
Ñ_{1} 
Cubic and Dimensional
a,b,[c]1 ≈> Eaf(a.,b..) :c1
Eaf

Second row

Beat nested arrays

Entry in hyperspace
a,a,[a,b]1 ≈> Eaf(a,b,[3]2)

The hyperrow
a,b,[,{c}1]1 ≈> Eaf(a,b,[c]2)
Ñ_{2} 
Dimensional separators
a,a,[Dim]1 ≈ Eaf(a,a,[Row]2)
Ñ_{3} 
Twice nested row
a,a,[,[Row]1]1 ≈ Eaf(a,a,[Dim]2)
Ñ_{4} 
Nesting depth
a,b.,[..]1 :c:
<≈ Eaf(a,b.,[1..]2.) :c:
Eaf

Entry in hyperspace

Btrix deep attachments

Dual deep

Serial deeps

Under Construction

Dual deep

Bigger

What is omega?
ω
*0 
Count from omega
ω..n
*1 
Byte box omega
2^ω
*2 
Walks past omega
ω^ω
*3

What is omega?

Omega jumps

Arrays of omega
G(ω)

Catching all reals
ω_{1}

Higher omega
Ω(a)

Omega pair on stairs
Ω(a,b)

Jump function Omega
Ω(a,Z)

Arrays of omega

Royal infinities

Jump recursion types
H(Ω_{t})

Heaven's gate

Jump recursion types
 Biggest
 Tables
Work draft © 2014 Giga Gerard