{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T09:54:01Z","timestamp":1772272441900,"version":"3.50.1"},"reference-count":14,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,1,1]]},"abstract":"<jats:title>Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences<\/jats:title>\n        <jats:p>Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept came from the individual Ergodic theorem (see [7]) and it is the preparation for its proof.<\/jats:p>","DOI":"10.2478\/v10037-008-0034-y","type":"journal-article","created":{"date-parts":[[2009,3,21]],"date-time":"2009-03-21T01:07:26Z","timestamp":1237597646000},"page":"283-288","source":"Crossref","is-referenced-by-count":2,"title":["Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences"],"prefix":"10.2478","volume":"16","author":[{"given":"Yatsuka","family":"Nakamura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hisashi","family":"Ito","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"1","first-page":"377","article-title":"Cardinal numbers","volume":"2","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"2","first-page":"41","article-title":"The fundamental properties of natural numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"3","first-page":"711","article-title":"Increasing and continuous ordinal sequences","volume":"4","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"4","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"5","first-page":"55","article-title":"Functions and their basic properties","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"6","first-page":"165","article-title":"Finite sets","volume":"1","author":"Agata Darmochwa\u0142","year":"1990","journal-title":"Formalized Mathematics"},{"key":"7","author":"Paul Halmos","year":"1956","journal-title":"Lectures on Ergodic Theory"},{"key":"8","first-page":"35","article-title":"Basic properties of real numbers","volume":"1","author":"Krzysztof Hryniewiecki","year":"1990","journal-title":"Formalized Mathematics"},{"key":"9","first-page":"269","article-title":"Real sequences and basic operations on them","volume":"2","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"10","first-page":"399","article-title":"Cardinal numbers and finite sets","volume":"3","author":"Karol P\u03b1k.","year":"2005","journal-title":"Formalized Mathematics"},{"key":"11","first-page":"341","article-title":"On the sets inhabited by numbers","volume":"4","author":"Andrzej Trybulec","year":"2003","journal-title":"Formalized Mathematics"},{"key":"12","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"13","first-page":"825","article-title":"Zero-based finite sequences","volume":"4","author":"Tetsuya Tsunetou","year":"2001","journal-title":"Formalized Mathematics"},{"key":"14","first-page":"73","article-title":"Relations and their basic properties","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/16\/3\/article-p283.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2008.16.issue-3\/v10037-008-0034-y\/v10037-008-0034-y.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:30Z","timestamp":1590852450000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-008-0034-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,1]]},"references-count":14,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/v10037-008-0034-y","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2008,1,1]]}}}