Experiment: Mapping real numbers between 0 to 1 to natural numbers

Re:Experiment: Mapping real numbers between 0 to 1 to natura... by neonskies on Thursday April 27, 2023 @08:49AM (#35727232)

Not sure what's on the vid. Didn't watch it. But if I understand you correctly, the following is impossible as shown in Cantor's simple diagonalization argument:

> Follow each branch as deeply as possible counting all sub branches until there are no sub branches left.

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Re:Experiment: Mapping real numbers between 0 to 1 to natura... by smac__ on Thursday April 27, 2023 @09:16AM (#35727606)

Good point, the depth first search algorithm is a bit lack luster for this case: 1 -> .1 2 -> .01 3 -> .001 4 -> .0001 5 -> .00001 6 -> .000001 . -> .0∞1

I would definitely recommend not judging the quality of the video based upon the quality of my reasoning in the experiment.

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Re:Experiment: Mapping real numbers between 0 to 1 to natura... by neonskies on Thursday April 27, 2023 @09:38AM (#35727940)

> 1 -> .1 2 -> .01 3 -> .001 4 -> .0001 5 -> .00001 6 -> .000001 . -> .0∞1

That would only count the rationals which you can definitely count off a carefully arranged matrix of rationals. But reals = rationals and irrationals and the irrationals are uncountable.

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Re:Experiment: Mapping real numbers between 0 to 1 to natura... by smac__ on Thursday April 27, 2023 @09:51AM (#35728095)

You are definitely right, I missed quite a few numbers in this set. (Thank you!)

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