“On the shoulders of giant numbers”
Think before you print.
Save the world's forests!
bigΨ.I. Number operations
bigΨ · part 1
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
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
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
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!