LEADER 04046nam 22006135 450 001 9910903795403321 005 20250808090205.0 010 $a9783031665455 010 $a3031665457 024 7 $a10.1007/978-3-031-66545-5 035 $a(MiAaPQ)EBC31755498 035 $a(Au-PeEL)EBL31755498 035 $a(CKB)36516547700041 035 $a(DE-He213)978-3-031-66545-5 035 $a(OCoLC)1467283292 035 $a(EXLCZ)9936516547700041 100 $a20241106d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPython Arithmetic $eThe Informational Nature of Numbers /$fby Vincenzo Manca 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (110 pages) 225 1 $aStudies in Big Data,$x2197-6511 ;$v153 311 08$a9783031665448 311 08$a3031665449 320 $aIncludes bibliographical references and index. 327 $aThe Origins of Digital Age -- Mathematical notation and Python -- Counting Algorithms in Python -- Arithmetic Operations -- Square Root Algorithms -- Primality, Equations, Congruences -- Symbolic Computation. 330 $aThe book is a gentle introduction to Python using arithmetic, and vice versa, with a historical perspective encompassing programming languages within the wider process of development of mathematical notation. The revisitation of typical algorithms that are the core of elementary mathematical knowledge helps to grasp their essence and to clarify some assumptions that are often taken for granted but are very profound and of a very general nature. The first mathematician to define a systematic system for generating numbers was Archimedes of Syracuse in the third century B.C. The Archimedean system, which was defined in a book with the Latin title Arenarius, was not intended to define all numbers, but only very large numbers [13, 22, 23]. However, it can be considered the first system with the three main characteristics of a counting system that have the most important properties for complete arithmetic adequacy: creativity, infinity, and recursion. Creativity means that each numeral is new for numerals that precede it; infinity means that after any numeral there is always another numeral; recursion means that after an initial sequence of numerals coinciding with the digits of the system, digits repeat regularly in all subsequent numerals. Since the numerals are finite expressions of digits, their lengths increase along their generation. In the next chapter, Python is briefly introduced by linking this language to standard mathematical notation, which took its current form throughout a long process that extends from the introduction of decimal numerals to the eighteenth century, particularly within Euler?s notational and conceptual framework. The third chapter is devoted to counting algorithms, showing that something that is usually taken for granted has intriguing aspects that deserve a very subtle analysis: the authors will show that the Python representation of counting algorithms is very informative and demonstrates the informational nature of numbers. 410 0$aStudies in Big Data,$x2197-6511 ;$v153 606 $aComputational intelligence 606 $aPython (Computer program language) 606 $aEngineering$xData processing 606 $aComputational Intelligence 606 $aPython 606 $aData Engineering 615 0$aComputational intelligence. 615 0$aPython (Computer program language) 615 0$aEngineering$xData processing. 615 14$aComputational Intelligence. 615 24$aPython. 615 24$aData Engineering. 676 $a004.0151 700 $aManca$b Vincenzo$067566 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910903795403321 996 $aPython Arithmetic$94272930 997 $aUNINA