Given irrational x, δ>0 ⱻ prime p s.t. δ>1/p. Let a/p!<x<(a+1)/p! and ε=min(|x-a/p!|,|x-(a+1)/p!|)/2 then for all x-ε<y<x+ε, f(y)<1/p<δ
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Also known as “Stars over Babylon”
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Still need to show that between a/p! and (a+1)/p! there are no rationals with denominator <=p (left as an exercise for the reader)
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Let the crisis begin!
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One of my favourite (counter)examples :-)
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I like popcorn...
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I liked popcorn...
End of conversation
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I wouldn’t have guessed that that was even possible.
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