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November 3rd, 2018, 07:16 AM   #1
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infinity of irrational numbers between i. numbers

How I prove that between irrational number there is infinity of irrational numbers?
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November 3rd, 2018, 07:40 AM   #2
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You can use the method suggested here.
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November 3rd, 2018, 10:03 AM   #3
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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...
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November 3rd, 2018, 02:01 PM   #4
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$p_2=(p_0+p_1)/2$, $p_3=(p_0+p_2)/2$, etc.
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November 3rd, 2018, 02:47 PM   #5
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Originally Posted by mathman View Post
$p_2=(p_0+p_1)/2$, $p_3=(p_0+p_2)/2$, etc.
$p_2$ is not necessarily irrational. e.g. $(p_0, p_1) = (\sqrt2, 2-\sqrt2)$,
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November 4th, 2018, 02:19 PM   #6
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Quote:
Originally Posted by v8archie View Post
$p_2$ is not necessarily irrational. e.g. $(p_0, p_1) = (\sqrt2, 2-\sqrt2)$,
You are right. I misread it as between rationals.
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