WM

2020-11-21 09:43:17 UTC

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PermalinkIndividual definition can occur

by direct description in the unary system like |||||||

or by the finite initial segment {1, 2, 3, 4, 5, 6, 7}

or in binary representation 111 or decimal representation 7

or by indirect description like "the number of colours of the rainbow"

or by other words known to sender and receiver like "seven".

Here are some articles about dark numbers:

Russia: Yaroslav D. Sergeyev: A new applied approach for executing computations with infinite and infinitesimal quantities, Informatica, 19 (2008), no. 4, 567–596.

Italy: Gabriele Lolli: Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation 255 (2015) 3–14

Russia: Yaroslav D. Sergeyev: Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems, EMS Surv. Math. Sci. 4 (2017), 219–320

Italy: Lorenzo Fiaschi, Marco Cococcioni: Numerical Asymptotic Results in Game Theory

Using Sergeyev’s Infinity Computing, Int. Journ. of Unconventional Computing, Vol. 14 (2018) pp. 1–25 Old City Publishing, Inc.

Norway: Davide Rizza: Numerical Methods for Infinite Decision-making Processes, Int. Journ. of Unconventional Computing, Vol. 14 (2019) pp. 139–158

Germany: Wolfgang Mückenheim: Dark natural numbers in set theory (2019)

https://www.researchgate.net/publication/336220780_Dark_natural_numbers_in_set_theory

Brazil: Walter Gomide: Dark Numbers Academia.edu (2020)

https://www.academia.edu/44462367/Dark_Numbers_academia_edu

Mew Zealand / Romania: Christian S. Calude, Monica Dumitrescu: Infinitesimal Probabilities Based on Grossone, SN Computer Science (2020)

Germany: Wolfgang Mückenheim: Transfinity - A Source Book (monthly updated), https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

A lecture about this topic will be given on Saturday, 21 Nov, 6 PM c.t. here:

https://hs-augsburg.zoom.us/j/92096767073?pwd=aG1DUzJOdnFqTzNTYk1FU0RFQUZ0QT09

Regards, WM