Zobrazeno 1 - 10
of 166
pro vyhledávání: '"Klazar, Martin"'
Autor:
Klazar, Martin
We develop a theory of real numbers as rational Cauchy sequences, in which any two of them, $(a_n)$ and $(b_n)$, are equal iff $\lim\,(a_n-b_n)=0$. We need such reals in the Countable Mathematical Analysis ([4]) which allows to use only hereditarily
Externí odkaz:
http://arxiv.org/abs/2308.04474
Autor:
Klazar, Martin
HMC sets are hereditarily at most countable sets. We rework a part of analysis of univariate real functions so that it (substantially) uses only HMC sets and present some applications. 1. By integrating functions $f\colon[u,v]_{\mathbb{Q}}= \{a\in\ma
Externí odkaz:
http://arxiv.org/abs/2301.08142
Autor:
Klazar, Martin
We investigate Bertrand's probabilistic paradox through the lens of discrete geometry and old-fashioned but reliable discrete probability. We approximate the plane unit circle with $1/n$ times $1/n$ boxes and count the pairs of boxes separated by dis
Externí odkaz:
http://arxiv.org/abs/2211.06749
Autor:
Klazar, Martin
We give a~detailed construction of the complete ordered field of real numbers by means of infinite decimal expansions. We prove that in the canonical encoding of decimals neither addition nor multiplication is {\em computable}, but that both operatio
Externí odkaz:
http://arxiv.org/abs/2108.02046
Autor:
Klazar, Martin, Horský, Richard
We answer the question in the title in the negative by providing four proofs.
Comment: To appear in AMM
Comment: To appear in AMM
Externí odkaz:
http://arxiv.org/abs/2107.10717
Autor:
Klazar, Martin
In order to state the theorem in the title formally and to review its rigorous proof, we extend and make more precise the Uspenskiy-Shen-Akopyan-Fedorov model of Euclidean constructions with arbitrary points; we also introduce formalizations for infi
Externí odkaz:
http://arxiv.org/abs/2107.09747
Autor:
Hančl Jr., Jaroslav, Klazar, Martin
For $k,l\ge2$ we consider ideals of edge $l$-colored complete $k$-uniform hypergraphs $(n,\chi)$ with vertex sets $[n]=\{1, 2, \dots n\}$ for $n\in\mathbb{N}$. An ideal is a set of such colored hypergraphs that is closed to the relation of induced or
Externí odkaz:
http://arxiv.org/abs/2005.10726
Autor:
Klazar, Martin
We propose a new definition of effective formulas for problems in enumerative combinatorics. We outline the proof of the fact that every linear recurrence sequence of integers has such a formula. It follows from a lower bound that can be deduced from
Externí odkaz:
http://arxiv.org/abs/2002.11964
Autor:
Hančl, Jaroslav, Jr., Klazar, Martin
Publikováno v:
In European Journal of Combinatorics October 2023 113
Autor:
Klazar, Martin
We present details of logically simplest integral sufficient for deducing the Stirling asymptotic formula for n!. It is the Newton integral, defined as the difference of values of any primitive at the endpoints of the integration interval. We review
Externí odkaz:
http://arxiv.org/abs/1907.02553