Przeglądaj według autora "Tyszka, Apoloniusz"
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2120297919943148946411837205892771504128704971219136 is greater than the total number of reachable positions in chess in which pawns are always in rows 2-7 and a non-fixed initial position has at most 32 pieces and is almost arbitrary
Tyszka, Apoloniusz (2023-01-11)A short MuPAD program shows that 2120297919943148946411837205892771504128704971219136 is greater than the total number of reachable positions in chess in which pawns are always in rows 2-7 and a non-fixed initial position ... -
On sets W \subseteq \mathbb{N} such that the infinity of W is equivalent to the existence in W of an element that is greater than a threshold number computed with using the definition of W
Tyszka, Apoloniusz (2018)Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n \geq 2. For a positive integer n, let \Theta_n denote the statement: if a system S \subseteq {x_i!=x_k: i,k \in {1,...,n}} \cup {x_i \cdot x_j=x_k: i,j,k \in ... -
Open mathematical problems which cannot be stated formally as they refer to intuitive meanings of mathematical formulae and the current mathematical knowledge
Tyszka, Apoloniusz (2020-01-26)Let \beta=((24!)!)!, and P_{n^2+1} denote the set of all primes of the form n^2+1. Let M denote the set of all positive multiples of elements of the set P_{n^2+1} \cap (\beta,\infty). The set X={0,...,\beta} \cup M satisfies ... -
Statements and open problems on decidable sets X⊆N that contain informal notions and refer to the current knowledge on X
Kozdęba, Agnieszka; Tyszka, Apoloniusz (2022)Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement ... -
The predicate of the current mathematical knowledge substantially increases the constructive and informal mathematics and why it cannot be adapted to any empirical science
Tyszka, Apoloniusz (Pi Mu Epsilon, 2023)This is a shortened and revised version of the article: A. Tyszka, Statements and open problems on decidable sets X⊆N, Pi Mu Epsilon J. 15 (2023), no. 8, 493-504. The main results were presented at the 25th Conference ... -
Theorems and open problems that concern decidable sets X \subseteq {\mathb N} and cannot be formalized in mathematics understood as an a priori science as they refer to the current knowledge on X
Kozdęba, Agnieszka; Tyszka, Apoloniusz (2022-02-21)Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. We present a new heuristic argument for the infiniteness of ...