"Je kontinuum skute\u010Dn\u011B nespo\u010Detn\u00E9?"@cs . . . "1"^^ . "\u010Cl\u00E1nek ukazuje problematiku p\u0159\u00EDstupu k matematick\u00E9mu a fyzik\u00E1ln\u00EDmu kontinuu v historick\u00E9m kontextu a otev\u00EDr\u00E1 ot\u00E1zku spr\u00E1vnosti, jedinosti a jednozna\u010Dnosti p\u0159\u00EDstupu sou\u010Dasn\u00E9ho. V \u00FAvodn\u00EDm odd\u00EDle je problematika kontinua p\u0159edstavena d\u00EDl\u010D\u00EDm probl\u00E9mem, kter\u00FD s kontinuem zd\u00E1nliv\u011B nesouvis\u00ED - Fibonacciho \u00FAlohou o v\u00E1\u017Een\u00ED. Ta n\u00E1s v\u0161ak inspiruje k %22u\u017Eite\u010Dn\u00E9mu%22, le\u010D komplikovan\u00E9mu p\u0159echodu od diskr\u00E9tn\u00EDho ke kontinu\u00E1ln\u00EDmu. T\u00EDm se ukazuje povaha konkr\u00E9tn\u00EDho fyzik\u00E1ln\u00EDho kontinua. Druh\u00FD odd\u00EDl p\u0159edstavuje Cantor\u016Fv p\u0159\u00EDstup k matematick\u00E9mu kontinuu, tvo\u0159en\u00E9mu re\u00E1ln\u00FDmi \u010D\u00EDsly, jejich\u017E nespo\u010Detnost demonstrujeme pomoc\u00ED tzv. Cantorovy diagon\u00E1ln\u00ED metody. Ta ov\u0161em skryt\u011B stoj\u00ED na p\u0159edpokladech, jejich\u017E spr\u00E1vnost nen\u00ED nutn\u00E1. Tyto nejednozna\u010Dn\u011B spr\u00E1vn\u00E9 p\u0159edpoklady (a jejich prot\u011Bj\u0161ky) jsou pak rozvedeny ve t\u0159et\u00EDm a \u010Dtvrt\u00E9m odd\u00EDle. Ji\u017E (a p\u0159edev\u0161\u00EDm) v dob\u011B sv\u00E9ho vzniku byla Cantorova teorie mno\u017Ein pod palbou kritiky. Ta je (neosobn\u011B a nedestruktivn\u011B - narozd\u00EDl od Cantorovy doby) na m\u00EDst\u011B i dnes. V p\u00E1t\u00E9m odd\u00EDl"@cs . "Je kontinuum skute\u010Dn\u011B nespo\u010Detn\u00E9?" . "320843" . . . "Is continuum really uncountable?"@en . "1"^^ . "RIV/49777513:23330/09:00502976!RIV10-MSM-23330___" . "RIV/49777513:23330/09:00502976" . . "Teorie a d\u011Bjiny v\u011Bdy a techniky" . "Je kontinuum skute\u010Dn\u011B nespo\u010Detn\u00E9?"@cs . "Z\u00E1pado\u010Desk\u00E1 univerzita v Plzni" . . "2009-06-27+02:00"^^ . "23330" . . "continuum; countability; B. Bolzano; G. Cantor; alternative"@en . . "978-80-7043-846-6" . . . "Plze\u0148" . . "Is continuum really uncountable?"@en . . . "The paper presents contemporary approaches to mathematical and physical continuum. It deals with a question of truth, oneness and definiteness of possible approaches. Fibonacci's problem of weigh-measuring introduces us into questions on relations between continuity and discreteness and evokes an interest about nature of physical continuum. On the other hand, contemporary mainstream approach to mathematical continuum - Cantor's one - is presented and the proof of its uncountability is given. Its debatable hidden presumptions are emphasized and discussed. We mention alternative approaches to continuum and to set theory at all. One possible approach to continuum is (very roughly) proposed. Here continuum is a domain, which allows any number, describable by finite numbers of words, to exist. Not only this countable continuum - it seems - is possible."@en . "Je kontinuum skute\u010Dn\u011B nespo\u010Detn\u00E9?" . "\u010Cl\u00E1nek ukazuje problematiku p\u0159\u00EDstupu k matematick\u00E9mu a fyzik\u00E1ln\u00EDmu kontinuu v historick\u00E9m kontextu a otev\u00EDr\u00E1 ot\u00E1zku spr\u00E1vnosti, jedinosti a jednozna\u010Dnosti p\u0159\u00EDstupu sou\u010Dasn\u00E9ho. V \u00FAvodn\u00EDm odd\u00EDle je problematika kontinua p\u0159edstavena d\u00EDl\u010D\u00EDm probl\u00E9mem, kter\u00FD s kontinuem zd\u00E1nliv\u011B nesouvis\u00ED - Fibonacciho \u00FAlohou o v\u00E1\u017Een\u00ED. Ta n\u00E1s v\u0161ak inspiruje k %22u\u017Eite\u010Dn\u00E9mu%22, le\u010D komplikovan\u00E9mu p\u0159echodu od diskr\u00E9tn\u00EDho ke kontinu\u00E1ln\u00EDmu. T\u00EDm se ukazuje povaha konkr\u00E9tn\u00EDho fyzik\u00E1ln\u00EDho kontinua. Druh\u00FD odd\u00EDl p\u0159edstavuje Cantor\u016Fv p\u0159\u00EDstup k matematick\u00E9mu kontinuu, tvo\u0159en\u00E9mu re\u00E1ln\u00FDmi \u010D\u00EDsly, jejich\u017E nespo\u010Detnost demonstrujeme pomoc\u00ED tzv. Cantorovy diagon\u00E1ln\u00ED metody. Ta ov\u0161em skryt\u011B stoj\u00ED na p\u0159edpokladech, jejich\u017E spr\u00E1vnost nen\u00ED nutn\u00E1. Tyto nejednozna\u010Dn\u011B spr\u00E1vn\u00E9 p\u0159edpoklady (a jejich prot\u011Bj\u0161ky) jsou pak rozvedeny ve t\u0159et\u00EDm a \u010Dtvrt\u00E9m odd\u00EDle. Ji\u017E (a p\u0159edev\u0161\u00EDm) v dob\u011B sv\u00E9ho vzniku byla Cantorova teorie mno\u017Ein pod palbou kritiky. Ta je (neosobn\u011B a nedestruktivn\u011B - narozd\u00EDl od Cantorovy doby) na m\u00EDst\u011B i dnes. V p\u00E1t\u00E9m odd\u00EDl" . . "S" . "14"^^ . "[781E3960E6E2]" . . "Kl\u00E1\u0161ter Tepl\u00E1" . "Chvojka, Ond\u0159ej" . . .