# Difference between revisions of "Talk:1516: Win by Induction"

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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. {{unsigned ip|108.162.229.177}} | 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. {{unsigned ip|108.162.229.177}} | ||

: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) | ||

"infinite, but countable" {Cough.} Someone doesn't understand infinity. Perhaps they meant "enumerable". [[Special:Contributions/108.162.250.155|108.162.250.155]] 09:29, 24 April 2015 (UTC) | "infinite, but countable" {Cough.} Someone doesn't understand infinity. Perhaps they meant "enumerable". [[Special:Contributions/108.162.250.155|108.162.250.155]] 09:29, 24 April 2015 (UTC) |

## Revision as of 12:37, 24 April 2015

Is the alt text a reference to double-yolkers (eggs with two yolks)? They're only about 1 in every 1000 but it seems like an obvious reference. --Fenn (talk) 08:32, 24 April 2015 (UTC)

- Makes sense to me. I didn't even think of double yolks until you mentioned it here. 173.245.50.89 09:04, 24 April 2015 (UTC)BK201

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. 108.162.229.177 (talk) *(please sign your comments with ~~~~)*

- Saw this too late. Yes, I agree, and I have fixed it accordingly. --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. 173.245.50.88 12:37, 24 April 2015 (UTC)

"infinite, but countable" {Cough.} Someone doesn't understand infinity. Perhaps they meant "enumerable". 108.162.250.155 09:29, 24 April 2015 (UTC)

- Someone doesn't understand countability. 141.101.89.217 09:46, 24 April 2015 (UTC)

"The front most Pikachu speaks." Hey, look, it has those little lines to show it's speaking, not the blank white space behind it. Duh. 108.162.250.155 09:32, 24 April 2015 (UTC)

Looks like Megan is looking at her watch as well. Mention in transcript/explanation? Fenn (talk) 09:34, 24 April 2015 (UTC)

- Are Megan and Cueball supposed to fight each other? It seems like Cueball still has his closed Pokéball in his hands. Is it then Megan's Pokéball that has evolved into all these Pikachu? And is it because she waits for her Pokémon to be ready to fight Cueball, that she checks her watch? I do not know anything about the Pokémon game/world. But it seems to me that some part of this setup is unexplained by the above... --Kynde (talk) 11:23, 24 April 2015 (UTC)

Friendly reminder: Grammatically speaking, Pokémon are like sheep or deer. Singular and plural are both written the same. One Pikachu, many Pikachu, all the Pikachu. You'd be surprised at how much rage forgetting this causes in certain corners of the Internet. 141.101.99.42 (talk) *(please sign your comments with ~~~~)*

What doesn't make sense to me is how this could continue indefinitely – after all, each of those Pikachu must have caught its own Pikachu beforehand. I don't see any infinite loop here, just a bunch of Pikachu that already had one another caught itselves. 141.101.96.217 10:13, 24 April 2015 (UTC)

The word "induction" could also be intended to have a double meaning, referring also to electromagnetic induction. Pikachu is, after all, and electric pokémon. 141.101.105.194 (talk) *(please sign your comments with ~~~~)*

- Yes, I think this is right. Something about Maxwell's equations and induction. 173.245.54.203 (talk)
*(please sign your comments with ~~~~)*- From an engineering standpoint, in my opinion, Pikachu act more like biological capacitors (stored electric charge at potentially high voltage able to deliver large discharge currents) than inductors ("storing" magnetic energy via constant current, able to deliver high voltage when interrupted, like the ignition coil for an older automotive engine). I'm not too familiar with the Pokémon in-game/in-show universe, but I would imagine the Nurse Jenny corps could use electric Pokémon such as Pikachu (or Raichu) like defibrillators for cardiac events! --BigMal // 173.245.50.177 11:42, 24 April 2015 (UTC)

There's a point floating about how infinity doesn't imply completion. For instance, the number of all even integers is infinite, yet any given integer "only has a 50% chance of being even", so the series is quite obviously incomplete. This article seems to tend towards the idea (in diction) that an infinite number of pikachu would result in a win based on a 'logical' premise, without referring specificially to the terms of it's assumption. Xerxesbeat (talk) 11:38, 24 April 2015 (UTC)

What happens if the Pikachu in the ball is recursing - picking himself? That doesn't fit the 30-40 double yolk thing, but would explain an infinite series. Food for thought. Megan is bored, waiting for the fight to start. I thought the game was supposed to begin when the players choose, though, so I don't understand why the wait is happening at all.

I doubt this is an intentional part of the joke, but the strongest Ground-type moves (Earthquake, Precipice Blades, etc.) are multi-target, hitting all foes in a 1v5 situation such as Horde Battles. In theory, a strong enough super effective move from Cueball's lead would still end the battle in one turn. 173.245.56.176 12:04, 24 April 2015 (UTC)