Arborescent numbers : higher arithmetic operations and division trees

The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2007

Author dc:creator

• Trappmann, Henryk

Contributors dc:contributor

• Denecke, Klaus-Dieter

• Tetration
• höhere Operationen
• strukturierte Zahlen
• Divisionsbäume
• higher operations
• structured numbers
• division trees

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1411

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:1411