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 November 3rd, 2018, 06:16 AM #1 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 infinity of irrational numbers between i. numbers How I prove that between irrational number there is infinity of irrational numbers? November 3rd, 2018, 06:40 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 You can use the method suggested here. Thanks from topsquark November 3rd, 2018, 09:03 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,685 Thanks: 2665 Math Focus: Mainly analysis and algebra If, between $p_0$ and $p_1$, there is a $p_2$, then between $p_0$ and $p_2$, there is a $p_3$, and between $p_0$ and $p_3$, there is a $p_4$, and between $p_0$ and $p_4$, there is a $p_5$, and... Thanks from topsquark November 3rd, 2018, 01:01 PM #4 Global Moderator   Joined: May 2007 Posts: 6,823 Thanks: 723 $p_2=(p_0+p_1)/2$, $p_3=(p_0+p_2)/2$, etc. Thanks from topsquark November 3rd, 2018, 01:47 PM   #5
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Quote:
 Originally Posted by mathman $p_2=(p_0+p_1)/2$, $p_3=(p_0+p_2)/2$, etc.
$p_2$ is not necessarily irrational. e.g. $(p_0, p_1) = (\sqrt2, 2-\sqrt2)$, November 4th, 2018, 01:19 PM   #6
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 Originally Posted by v8archie $p_2$ is not necessarily irrational. e.g. $(p_0, p_1) = (\sqrt2, 2-\sqrt2)$,
You are right. I misread it as between rationals. Tags infinity, irrational, numbers Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Pengkuan Math 61 February 29th, 2016 04:46 PM Pengkuan Math 47 January 14th, 2016 12:56 PM Albert.Teng Algebra 4 February 12th, 2014 04:55 PM Mighty Mouse Jr Algebra 1 October 16th, 2010 07:46 PM MattJ81 New Users 11 July 10th, 2010 07:51 PM

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