Epsilon Numbers and Cantor Normal Form

Grzegorz Bancerek. "Epsilon Numbers and Cantor Normal Form." Formalized Mathematics 17.4 (2009): 249-256. <http://eudml.org/doc/266687>.

@article{GrzegorzBancerek2009,
abstract = {An epsilon number is a transfinite number which is a fixed point of an exponential map: ωϵ = ϵ. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: [...] and for limit ordinal λ: [...] Tetration stabilizes at ω: [...] Every ordinal number α can be uniquely written as [...] where κ is a natural number, n1, n2, …, nk are positive integers, and β1 > β2 > … > βκ are ordinal numbers (βκ = 0). This decomposition of α is called the Cantor Normal Form of α.},
author = {Grzegorz Bancerek},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {249-256},
title = {Epsilon Numbers and Cantor Normal Form},
url = {http://eudml.org/doc/266687},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Grzegorz Bancerek
TI - Epsilon Numbers and Cantor Normal Form
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 4
SP - 249
EP - 256
AB - An epsilon number is a transfinite number which is a fixed point of an exponential map: ωϵ = ϵ. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: [...] and for limit ordinal λ: [...] Tetration stabilizes at ω: [...] Every ordinal number α can be uniquely written as [...] where κ is a natural number, n1, n2, …, nk are positive integers, and β1 > β2 > … > βκ are ordinal numbers (βκ = 0). This decomposition of α is called the Cantor Normal Form of α.
LA - eng
UR - http://eudml.org/doc/266687
ER -