Article by G.F. Romerio<\/a>\u00a0in the forum \u00aba New Kind of Science\u00bb of www.wolframscience.com<\/p>\n Abstract<\/p>\n
[et_pb_section fullwidth=\u00bbon\u00bb background_color=\u00bb#8224e3″ inner_shadow=\u00bboff\u00bb parallax=\u00bboff\u00bb][et_pb_fullwidth_header admin_label=\u00bbFullwidth Header\u00bb background_layout=\u00bbdark\u00bb text_orientation=\u00bbleft\u00bb title=\u00bbZeroth-rank operation and non transitive numbers\u00bb \/][\/et_pb_section][et_pb_section][et_pb_row][et_pb_column type=\u00bb3_4″][et_pb_text admin_label=\u00bbText\u00bb background_layout=\u00bblight\u00bb text_orientation=\u00bbleft\u00bb]<\/p>\n
Download the pdf from the website Arxiv:\u00a0http:\/\/arxiv.org\/abs\/1205.1703<\/a><\/p>\n Article by G.F. Romerio<\/a>\u00a0in the forum \u00aba New Kind of Science\u00bb of www.wolframscience.com<\/p>\n Abstract<\/p>\n
![\"FormulaEuleroStigmaZero\"](\"https:\/\/www.cescoreale.com\/wp-content\/uploads\/2014\/02\/FormulaEuleroStigmaZero.png\")
<\/a>Observing the existing relationships between the elementary operations of addition, multiplication (iteration of additions) and exponentiation (iteration of multiplications), a new operation (named incrementation) is defined, consistently with these laws and such that addition turns out to be an iteration of incrementations. Incrementation turns out to be consistent with Ackermann’s function. After defining the inverse operation of incrementation (named decrementation), we observe that R is not closed under it. So a new set of numbers is defined (named E, Escherian numbers), such that decrementation is closed on it. After defining the concept of pseudoorder (analogous to the order, but not transitive), addition and multiplication on E are analysed, and a correspondence between E and C is found. Finally, incrementation is extended to C, in such a way that decrementation is closed on C too. English keywords: hyper-operations, incrementation, zeration, Ackermann function, intransitive order, not transitive order, intransitive numbers, non transitive numbers, not transitive numbers, new number sets.<\/p>\n![\"PseudoordinamentoDeiComplessi-5\"](\"https:\/\/www.cescoreale.com\/wp-content\/uploads\/2014\/02\/PseudoordinamentoDeiComplessi-5.jpg\")
<\/a><\/p>\n