Sergeyev, Y.D. (2015) Computations with Grossone-Based Infifinities. In: Calude, C. and Dinneen, M., Eds., Unconventional Computation and Natural Computation, UCNC 2015, Lecture Notes in Computer Science, Springer, Cham, 89-106.
https://doi.org/10.1007/978-3-319-21819-9_6

has been cited by the following article:

• TITLE: Hilbert’s First Problem and the New Progress of Infinity Theory

  AUTHORS: Xijia Wang

  KEYWORDS: Hilbert’s First Problem, Cardinal Numbers Method, Grossone Method, Continuum Paradox, Infinity Theory

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.4, April 18, 2023

  ABSTRACT: In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.