X-Received: by 10.13.212.132 with SMTP id w126mr3047181ywd.57.1449145312145; Thu, 03 Dec 2015 04:21:52 -0800 (PST) X-Received: by 10.140.94.151 with SMTP id g23mr174795qge.12.1449145312120; Thu, 03 Dec 2015 04:21:52 -0800 (PST) Path: news.ccsf.jp!tomockey.ddo.jp!feeder.erje.net!1.us.feeder.erje.net!enother.net!enother.net!peer01.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!b51no6106256qgf.0!news-out.google.com!f23ni20958qge.0!nntp.google.com!f78no6105283qge.1!postnews.google.com!glegroupsg2000goo.googlegroups.com!not-for-mail Newsgroups: fj.education.math Date: Thu, 3 Dec 2015 04:21:51 -0800 (PST) Complaints-To: groups-abuse@google.com Injection-Info: glegroupsg2000goo.googlegroups.com; posting-host=82.243.43.32; posting-account=W5eYrwoAAAB5V1XeuIH0Ow4LYs9cI3X3 NNTP-Posting-Host: 82.243.43.32 User-Agent: G2/1.0 MIME-Version: 1.0 Message-ID: Subject: Cardinality of the set of binary-expressed real numbers From: PengKuan Em Injection-Date: Thu, 03 Dec 2015 12:21:52 +0000 Content-Type: text/plain; charset=ISO-8859-1 X-Received-Bytes: 1794 X-Received-Body-CRC: 1693767073 Xref: news.ccsf.jp fj.education.math:339 This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor's diagonal argument, power set and the continuum hypothesis. 1. Counting the fractional binary numbers 2. Fractional binary numbers on the real line 3. Countability of BF 4. Set of all binary numbers, B 5. On Cantor's diagonal argument 6. On Cantor's theorem 7. On infinite digital expansion of irrational number 8. On the continuum hypothesis Please read the article at Cardinality of the set of binary-expressed real numbers http://pengkuanonmaths.blogspot.com/2015/12/cardinality-of-set-of-binary-expressed.html or https://www.academia.edu/19403597/Cardinality_of_the_set_of_binary-expressed_real_numbers