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edit approved May 24, 2019 at 17:00
Adam Chalumeau
edit approved May 24, 2019 at 17:00
Adam Chalumeau
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Let S$S$ be the set {0, 1}$\{0, 1\}$. Given any subset of S$S$ we may add its arithmetic mean to S$S$ (provided it is not already included - S$S$ never includes duplicates). Show that by repeating this process we can include the number 1/5$1/5$ in S$S$. Show that we can eventually include any rational number between 0$0$ and 1$1$.

Let S be the set {0, 1}. Given any subset of S we may add its arithmetic mean to S (provided it is not already included - S never includes duplicates). Show that by repeating this process we can include the number 1/5 in S. Show that we can eventually include any rational number between 0 and 1.

Let $S$ be the set $\{0, 1\}$. Given any subset of $S$ we may add its arithmetic mean to $S$ (provided it is not already included - $S$ never includes duplicates). Show that by repeating this process we can include the number $1/5$ in $S$. Show that we can eventually include any rational number between $0$ and $1$.

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Saurabh Shukla
Saurabh Shukla
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Means and Set of Rational Numbers

Let S be the set {0, 1}. Given any subset of S we may add its arithmetic mean to S (provided it is not already included - S never includes duplicates). Show that by repeating this process we can include the number 1/5 in S. Show that we can eventually include any rational number between 0 and 1.