аЯрЁБс>ўџ 8:ўџџџ7џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅСq`№ПKbjbjqPqP.$::ч cџџџџџџЄ ( 444HL L L 8„ $Ј HWіШ Ш Ш о о Й Й Й жииииии$MhЕVќ4М Й Й М М ќ44о о лњњњМ В4о 4о жњМ жњњ44њо М `vюЦL nšњВ$'0Wњ ˆ њњX 4R`Й Z @њS 4‡ 5Й Й Й ќќjЙ Й Й WМ М М М HHHL HHHL HHH444444џџџџ BOOK REPORTS Arithmetic of Infinity by Yaroslav D. Sergeyev Edizioni Orizzonti Meridionali, 2003, 112 pp. ISBN 88-89064-01-3 Prof. Yaroslav Sergeyev (Universitр della Calabria, Italia) introduces a novel and exciting paradigm of computations with infinite and infinitesimal numbers. He proposes a new infinite unit of measure to operate with infinity as entity not process, develops a powerful positional numeral system with an infinite radix, and shows that many of mathematical paradoxes related to infinity arise rather from inadequate numeral systems, traditionally used to represent numbers, than from nature of infinity. The power of the new methodology is illustrated in the book by several examples and simple natural solutions to several famous paradoxes related to problems of infinity, including Thompson Lamp Paradox and Hilbert’s Paradox of the Grand Hotel. By introducing different infinite numbers the author manages to avoid undetermined forms emerging in traditional calculus operating with infinity, to calculate sums of and implement arithmetical operations on divergent series, and to introduce physical notion of a point in mathematics. Moreover, the infinite numbers introduced in the book possess cardinal and ordinal characteristics similarly to finite numbers. Being high-profile expert in numerical algorithms, number and set theories, and non-standard analysis, Sergeyev negotiates complexity of the subject by appealing to intuitive thinking, physics-based reality and real-life examples. For example, he demonstrated several techniques of aboriginal counting of objects which uses not one but several units of measure, related to each other as `infinite’ and `infinitesimal’; this type of counting was used by human beings for thousands of year but has never before been incorporated in mathematics and computer science methodologies. The book is attractive not only due its insightful theoretical results, related to some of the most challenging problems in mathematics, as the first Hilbert problem, but also in real possibility to use the new calculus in very near future. The author has already filed an international patent on the Infinity Computer which implements arithmetical operations with infinite and infinitesimal numbers. These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used. This reader-friendly introduction to an unconventional paradigm of computation with numbers will open new horizons in calculus and modeling, and will make a significant contribution to advances of mathematics, computer science and physics. Andrew Adamatzky, Editor-in-Chief University of the West of England Bristol BS16 1QY, UK  A simple simulator of the Infinity Computer already exists and the first application -- Infinity Calculator – using the Infinity Computer technology can be viewed at  HYPERLINK "http://www.theinfinitycomputer.com" http://www.theinfinitycomputer.com     International Journal of Unconventional Computing, Volume 2, Issue 2, 2006, 193-194.  &)12>?_`fmn‚ƒ„ОПРЭжьїM i t } С Т к єщзщЩЛЩщЩАщАЩАЩЃ–ŒŒukakTaŒaŒaŒahе]hХfёCJmH sH hХfёCJmH sH hslіCJmH sH hnтCJmH sH hšg[hБQACJmH sH hБQACJmH sH hѓ|йhaBCJmH sH hѓ|йhaBCJmH sH hnт5CJmH sH hЁ'PhvPK5CJmH sH hЁ'PhaB5CJmH sH "hMhM5;CJaJmH sH hM5CJmH sH hЊeŠ5CJmH sH   &?`o‚ƒ„z  Sš‹ŒЏвчцчщњњњњњњњњњђцожооЮТТТРОО $„}^„}a$gd„`‰$a$gdW8Т$a$gd0=c$a$gdLs $„`„a$gdБQA$a$gdšg[$a$ччJ§§§к № ё ћ   " * 1 2 3 A F H I Q R . C  і Щїќ "#23;<BPSуфцŽ™šŠ‹іщпщівівівівіХівіИіЎЄЎЄЎЄЎЄЎЄЎЄЎЄЎšŠš€v€Є€Ўh8$>CJmH sH h&CJmH sH jhO^0JCJUmH sH hO^CJmH sH h0=cCJmH sH hLsCJmH sH h ^hБQACJmH sH hhБQACJmH sH h№mЎhБQACJmH sH hХfёCJmH sH h№mЎhХfёCJmH sH hБQACJmH sH +‹ŒЏбвцчшщ>A~‹РСуфхцчшъыэю№ёіьобібФКЏЄœЄ”œ‰~‰qbX~TLTLTLTLjh`!Uh`!h8$>CJmH sH jhO^h8$>UmH sH hO^h8$>0JmH sH hO^h8$>mH sH jhO^h8$>UhззmH sH h8$>mH sH hO^h8$>mH sH hззh8$>mH sH jh8$>0JUh„`‰hжNїCJmH sH h„`‰h„`‰CJmH sH h„`‰h„`‰5CJmH sH hf`CJmH sH h„`‰CJmH sH щъьэя№ђѓHIJK§§§§§§§ј§§ь $„}^„}a$gd„`‰gd„`‰ ёѓ67=GHIJKќяхялязќЪh„`‰hжNїCJmH sH hЦUЯh]xdCJmH sH h„`‰CJmH sH h„`‰h„`‰CJmH sH h`! ,PАƒ. АШA!АŠ"АŠ#Š$Š%ААаАа а†œ>@ёџ> 1KG=K9CJ$_HmHsHtHBA@ђџЁB A=>2=>9 H@8DB 0170F0\iѓџГ\ 1KG=0O B01;8F0 :V і4ж4ж laі .kєџС. 5B A?8A:0 ‚e@ђ‚ vPK!B0=40@B=K9 HTML7 Ц2”(М Pфx  4 Ш#\'№*„.2Ќ5@9CJOJQJ^J:U@Ђ: ]mX 8?5@AAK;:0 >*B*phџ8@8 O^ "5:AB A=>A:8CJ2&@Ђ!2 O^ =0: A=>A:8H*L^@2L „`‰ 1KG=K9 (251)ЄdЄd[$\$CJaJL@BL „`‰5@E=89 :>;>=B8BC;  ЦгІ%J @RJ „`‰86=89 :>;>=B8BC;  ЦгІ%VV@ЂaV Є №@>A<>B@5==0O 38?5@AAK;:0 >*B* ph€€уK џK $џџџџ &?`o‚ƒ„zSš ‹ Œ  Џ в ч ц ч щ ъ ь э я № ђ ѓ H I L ˜0€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜@0€€00џ˜@0€€Iˆ00Љ˜@0€€Iˆ00Љ˜@0€€Iˆ00Љ˜@0€€Iˆ00Љ˜@0€€IШ00 ћЊIˆ00,Љ bbbbbeк ‹ёK щK J ЈйќXŒ№8№@ёџџџ€€€ї№’№№0№( № №№B №S №ПЫџ ?№џџА” ,:§Б” ”EѕВ” ЄіГ” D іД” dШ#Е” $іЩ Щ в в к ф L а а й т ц ц L >*€urn:schemas-microsoft-com:office:smarttags €PostalCode€8*€urn:schemas-microsoft-com:office:smarttags€City€B*€urn:schemas-microsoft-com:office:smarttags€country-region€9*€urn:schemas-microsoft-com:office:smarttags€place€ Ф@­ ?GHQR]ЇЈ­”  ц ч ц ч ч щ щ ъ ъ ь э я № ђ ѓ I L &(`mЈ­СЩ† Ž ч ч ч щ щ ъ ъ ь э я № ђ ѓ I L 33333%&?ц ч ч ч ш щ щ ъ ъ ы ь э я № ђ ѓ I L ц ч ц ч ч щ щ ъ ъ ь э я № ђ ѓ I L ЋbЧХb -@ Хb а+х'tRRхQCQz&`!!7Ц_# aBГ!sj(ЭZ$hv)|=8$>БQAvPKMЁ'PбcPД.Q R]mX~Y†"[šg[7]\ ^O^7_@ _f`0=c]xd…mƒrLssvЖ>yXz!|’N€a‡„`‰ЊeŠЃCx+Žn‰)е]‹0”#'›%jЃнAЌ})В )ГIWДюИIК ^СW8ТŸ[ЫЦUЯє#аВдfжззDOиѓ|йnт0hцœ юЄ №Хfёл&є@MѕslіжNїSљНќ i§Џ ч ф L џ@€ќ№CK `@џџUnknownџџџџџџџџџџџџGЬ‡z €џTimes New Roman5€Symbol3&Ь ‡z €џArial?5Ь ‡z €џCourier New"1ˆ№у;гІ&;гІ&\ЄF G  G !№ЅРДД€4dт т 2ƒq№ппHX№џ?фџџџџџџџџџџџџџџџџџџџџџ )Г2џџ Yaroslav DandrewNastyaўџр…ŸђљOhЋ‘+'Гй0p˜ЌИШдф є  , 8 DPX`hу Yaroslav DandrewNormalNastya2Microsoft Office Word@^аВ@f0™_]Ц@ЂСУў˜Ц@ЂСУў˜Ц G ўџеЭеœ.“—+,љЎDеЭеœ.“—+,љЎ8є hp|„Œ” œЄЌД М гут ц  Yaroslav D  ЭрчтрэшхШ 8@ _PID_HLINKSуA€r:$http://www.theinfinitycomputer.com/к  ўџџџўџџџ !"#$%&ўџџџ()*+,-.ўџџџ0123456ўџџџ§џџџ9ўџџџўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ РFPјпў˜Ц;€Data џџџџџџџџџџџџ1Tableџџџџ WordDocumentџџџџ.$SummaryInformation(џџџџџџџџџџџџ'DocumentSummaryInformation8џџџџџџџџ/CompObjџџџџџџџџџџџџqџџџџџџџџџџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџ џџџџ РFФюъѓьхэђ Microsoft Office Word MSWordDocWord.Document.8є9Вq