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"Far away, in the heavenly abode of the great god Indra, there is a wonderful net that has been hung by some artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each "eye"of the net, and since the net itself is infinite in dimension, the jewels are infinite in number. If we new arbitrarily select one of the jewels and inspect it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is reflecting all the others, so there is an infinite reflecting process occurring."

Is the number of jewels + jewel reflections countably infinite or not? How do I prove it?


marked as duplicate by Henning Makholm, user147263, Daniel W. Farlow, Davide Giraudo, Rory Daulton Dec 22 '15 at 0:01

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    $\begingroup$ The set being described can be indexed by $\Bbb N^{\Bbb N}$, which is uncountably infinite. $\endgroup$ – Omnomnomnom Sep 15 '14 at 16:18
  • $\begingroup$ Yay! Applying math to non-mathematical Buddhist metaphors! $\endgroup$ – Asimov Sep 15 '14 at 16:23
  • $\begingroup$ Could you explain in smaller steps why ℕ^ℕ is uncountably infinite or direct me to a website that could explain it? $\endgroup$ – Campbell Hutcheson Sep 15 '14 at 21:50

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