76 citations · 631 across the 35 of their papers we have counts for
10 papers · 1 filter
Lower and upper estimates of the quantity of algebraic numbers
Yaroslav D. Sergeyev
It is well known that the set of algebraic numbers (let us call it ) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cant…
Some paradoxes of Infinity revisited
Yaroslav D. Sergeyev
In this article, some classical paradoxes of infinity such as Galileo's paradox, Hilbert's paradox of the Grand Hotel, Thomson's lamp paradox, and the rectangle paradox of Torricel…
Independence of the grossone-based infinity methodology from non-standard analysis and comments upon logical fallacies in some texts asserting the opposite
Yaroslav D. Sergeyev
This commentary considers non-standard analysis and a recently introduced computational methodology based on the notion of \G1 (this symbol is called \emph{grossone}). The latter a…
The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area
Yaroslav D. Sergeyev
The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite…
On existence of infinite primes and infinite twin primes
Maurice Margenstern, Yaroslav D. Sergeyev
The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not rela…
On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function
Yaroslav D. Sergeyev
The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Rieman…