#
*“On the shoulders of giant numbers”*

http://www.iteror.org/big/book/main/part1.html
*Think before you print.*

Save the world's forests!
big**Ψ**

http://www.iteror.org/big/book/main/part1.html

Save the world's forests!

# bigΨ.I. Number operations

#####
bigΨ · part 1

*edit 0.2.9*

#### §I.0. Prelude

Finite beings can only build *finite* systems.
In mathematics we often assume otherwise, but to reasonably refer to
infinite

items we need to keep our conversation *finite*,
else nobody could hear us out.

To paraphrase the great
Dedekind
– is he listening? – a mathematical system is Big

when it is similar to a previous part of itself.
Something as simple as adding an extra counter
will expand upon an algorithm for Big numbers
to create mind-bogglingly Bigger ones…

In our own number constructions the initial operators are made to
*nearly match* the later operatorial functions.
As often, this requires a *jump* out of the box and into the ocean

.
When jump and match satisfy, previous concepts are ready to be counted
in a new and higher, more general system.

Each number finds expression in some system of words and belongs to one of six different temperaments – four of man and two of the divine.

- Address numbers
- to point to quantities or chances in the physical world
- Big numbers
- expressions reduced by an algorithm to a series of units
- Continuous numbers
- the algorithm never halts, projected to the real or infinite
- Diametric numbers
- records that mark the jump to hitherto disparate levels
- Endless numbers
- various types of infinity derived by infinite functions
- Fantastic numbers
- these can only be understood by a philosopher

This on-line book is about the quest for the Biggest numbers
and their construction tools – the operatorials bigO.
Functions which produce theoretically countable,
but practically uncountable *natural numbers* `1..`

The sign `ψ`

(psi)
was used by the recursion theorist Wilhelm Ackermann to mark a
*higher type* of function, iterating over a known family of functions.
Therefore our prodigious paper is delivered with the tantalizing title
`bigΨ`

.

Also this `ψ`

we conjure is kind of a running gag
throughout the book – a number too ... to fantasize about.

*We wish all readers a giant leap and an enchanting journey,
into a boundless land of numbers untold of before!*

## Diophantine riddle

Asamkhyeya dâsa takes the liberty to start with a numerological riddle:

The background-coloured digits in the following number point to a

diophantine equation. What is its formula?{click→}{hint→}666 does seem to be the last solution in number base 10, and there are probably no diophantine solutions with more than 5 digits in any other radix. But beware! As foretold in a secret Sasataansanic saga, there might be a Big number solution with 6 digits in the true number basket of Kabbalah, where Tetragrammaton and Beast Nº.2*333 rest asleep in a sea of glass mixed with fire – humånity hanging upside down from Yggdrasil, the mångrove Church of Life, like a Lemån — whose diophantine equation is…`(a+b)*(a-b)+a = b*(r^p-1)/(r-1)`

{b<r}