Paper Info
Title
Epsilon Numbers And Cantor Normal Form
Abstract
An epsilon number is a transfinite number which is a fixed point of an exponential map: omega(epsilon) = epsilon. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, up arrow up arrow). Namely, the ordinal indexing of epsilon numbers is defined as follows:epsilon(0) = omega up arrow up arrow omega, epsilon(alpha+1) = epsilon(alpha)up arrow up arrow omega,and for limit ordinal lambda:epsilon(lambda) = lim(alpha <lambda) epsilon(alpha) = U-alpha <lambda epsilon(alpha). Tetration stabilizes at omega :alpha up arrow up arrow beta = alpha up arrow up arrow omega for alpha not equal 0 and beta >= omega.Every ordinal number alpha can be uniquely written asn(1)omega(beta 1) + n(2)omega(beta 2) + .... + n(k)omega(beta k),where k is a natural number, n(1), n(2), ..., n(k) are positive integers, and beta(1) > beta(2) > ... > beta(k) are ordinal numbers (beta(k) = 0). This decomposition of alpha is called the Cantor Normal Form of alpha.
Year
DOI
Venue
2009
10.2478/v10037-009-0032-8
FORMALIZED MATHEMATICS
Keywords
Field
DocType
m,n,normal form
Discrete mathematics,Epsilon numbers,Mathematics
Journal
Volume
Issue
ISSN
17
4
1898-9934
Citations 
PageRank 
References 
1
0.43
0
Authors
1
Name
Order
Citations
PageRank
Grzegorz Bancerek19619.74