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November 3rd, 2018, 07:16 AM  #1 
Senior Member Joined: Nov 2011 Posts: 247 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, 10:03 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 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...

November 3rd, 2018, 02:01 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,661 Thanks: 648 
$p_2=(p_0+p_1)/2$, $p_3=(p_0+p_2)/2$, etc.

November 3rd, 2018, 02:47 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra  
November 4th, 2018, 02:19 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,661 Thanks: 648  

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