Rules of building the "tree of fractions": 0. Start from 1/1. 1. Left child of m/n is m/(m+n). 2. Right child of m/n is (m+n)/n.
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I proved this in an exam question in CS and the approach I chose was different. I showed a coordinate space of numerators along Y and denominators along X and walked outward from the origin in a spiral diamond. I think my approach is more intuitive because it’s visual :)
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@hadleguy Look how cool this is! Better than counting diagonally because you don't need to omit repeated valuesThanks. Twitter will use this to make your timeline better. UndoUndo
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Amusant Recyclage en exo envisagé ;-)
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You omitted zero and negative numbers though, those are also rational.
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It's just that countable infinity twice and then you add one for the 0, which ends up still at a countable infinity
End of conversation
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This Is really elegant but my favorite visual proof is the counterexample to the statement that real numbers are countable.
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The stern brocot tree!
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Stern-brocot tree
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