Editing Talk:1516: Win by Induction
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:::I'd think it's a reference to the rate of twins, which is currently almost exactly 1/30 (and on the rise) [http://en.wikipedia.org/wiki/Twin#Statistics] [[Special:Contributions/173.245.56.186|173.245.56.186]] 17:45, 24 April 2015 (UTC)Merkky[[Special:Contributions/173.245.56.186|173.245.56.186]] 17:45, 24 April 2015 (UTC) | :::I'd think it's a reference to the rate of twins, which is currently almost exactly 1/30 (and on the rise) [http://en.wikipedia.org/wiki/Twin#Statistics] [[Special:Contributions/173.245.56.186|173.245.56.186]] 17:45, 24 April 2015 (UTC)Merkky[[Special:Contributions/173.245.56.186|173.245.56.186]] 17:45, 24 April 2015 (UTC) | ||
− | The explanation currently says that doubling makes it uncountably infinite. I'm pretty sure that doubling at each step (or every few steps) is still a countable infinite set. Proof here: http://practicaltypography.com/the-infinite-pixel-screen.html (see section "The internet demands a recount", because the first attempt is wrong). We can also prove it using the same argument as when proving that N x N is countable infinite (making zig-zag), but in this case making a breadth-first search of the tree of Pikachus: map 1 to the first Pikachu, map 2 and 3 to the two Pikachus at the second level, map 4, 5, 6, 7 to the four Pikachus at the third level, map (2^(n-1))…((2^n) - 1) to the 2^(n-1) Pikachus at level n. | + | The explanation currently says that doubling makes it uncountably infinite. I'm pretty sure that doubling at each step (or every few steps) is still a countable infinite set. Proof here: http://practicaltypography.com/the-infinite-pixel-screen.html (see section "The internet demands a recount", because the first attempt is wrong). We can also prove it using the same argument as when proving that N x N is countable infinite (making zig-zag), but in this case making a breadth-first search of the tree of Pikachus: map 1 to the first Pikachu, map 2 and 3 to the two Pikachus at the second level, map 4, 5, 6, 7 to the four Pikachus at the third level, map (2^(n-1))…((2^n) - 1) to the 2^(n-1) Pikachus at level n. |
:Saw this too late. Yes, I agree, and I have fixed it accordingly. --[[User:Stephan Schulz|Stephan Schulz]] ([[User talk:Stephan Schulz|talk]]) 09:28, 24 April 2015 (UTC) | :Saw this too late. Yes, I agree, and I have fixed it accordingly. --[[User:Stephan Schulz|Stephan Schulz]] ([[User talk:Stephan Schulz|talk]]) 09:28, 24 April 2015 (UTC) | ||
:The problem being that we don't have an exact number for how many steps include double Pikachus. Granted, this is just a problem of practice, not theory. [[Special:Contributions/173.245.50.88|173.245.50.88]] 12:37, 24 April 2015 (UTC) | :The problem being that we don't have an exact number for how many steps include double Pikachus. Granted, this is just a problem of practice, not theory. [[Special:Contributions/173.245.50.88|173.245.50.88]] 12:37, 24 April 2015 (UTC) |