# Talk:1516: Win by Induction

In Pokemon games from Gold and up, pokemon are able to hold items, including pokeballs. While in the game, once a pokeball is filled it is no longer available to select as an item, this comic would seem to imply the possible 'inception' scenario of having a pokemon hold an active pokeball (as the games have already shown that a pokeball can go into a pokeball). --173.245.54.193 14:13, 24 April 2015 (UTC)

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
Seconded. --188.114.110.52 14:34, 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. 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)
enumeration is counting, in the simplest sense. "To name one by one; specify, as if in a list". That said, the whole of infinite whole numbers CAN be counted, just not by a human and not within a reasonable amount of time. --188.114.110.52 14:34, 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 ~~~~)

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 are certain moves, including some that Pikachu can learn, that appear to be based on induction (Thunder Wave and Shock Wave). Besides, they build up charge in their bodies from somewhere; I'd suspect induction from the surrounding environment is what charges them up. --188.114.110.52 14:34, 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)

Not Land's Wrath, Dig, or Earth Power, which are strong ground-type moves.173.245.48.126 13:05, 24 April 2015 (UTC)

I normally get a hearty chuckle out of Randall's graphical musings, but this one had me scratching my head. Fortunately, ExplainXKCD always comes to the rescue! After reading this page, my first thought was: Pokéception! 13:17, 24 April 2015 (UTC)

## Induction

Two other possibilities: one, in a bit of googling, it would appear that there is a type of Pokémon evolution called induced evolution, which involves stones of some kind? Alternately, we can use the term induction in the sense of soneone being inducted into a group. In this case, Megan has trained her Pikachu to be a Pokémaster. (Perhaps by arranging for it to be inducted into a rarified "gym"? I confess, I know nothing about the show.) 173.245.56.196 13:11, 24 April 2015 (UTC)

I'm surprised no one mentioned that Pokémon is a game a long time before becoming a show. Although it was because of the animated series that Pikachu became "special" among the hundreds of other cute critters.

Also, no mention to the russian matryoshka dolls? Come on... Closest other xkcd I recall is https://xkcd.com/878/

## Axiom of choice

Could this be to do with the axiom of choice from set theory? From my understanding, it's a fundamental axiom of set theory that says 'given a set of sets, it's possible to choose one element from each of those sets'. "Choosing" is in this case a specific operation that can be performed on an element.

One specific detail about the axiom is that all sets under consideration must be nonempty; that is, they must contain at least one element. So I think this is analogous to the situation of a Pokemon trainer owning multiple (full) Pokeballs: his Pokeballs are a collection of non-empty sets from which he is now trying to choose a single element ("Pikachu, I choose you!").

Under normal circumstances, he can do this without invoking the axiom of choice because he knows the names of all his Pokemon and so can select one from each set. In this case, he could prove his ability to make the choice simply by releasing all of his Pokemon from their balls one at a time. (The Pokemon's name is actually irrelevant, because simply releasing the Pokemon counts as a choice).

However, the situation becomes more complex if it turns out that his Pokemon also possess Pokeballs, because now his ability to make the choice is uncertain. In this situation, there could be infinitely many Pikachus, and so he can't definitely select a Pikachu from all the Pokeballs under his control. In a situation like this, a mathematician would invoke the axiom of choice.

However, it seems that Cueball is actually having a go at it using an inductive method of choice: first by choosing a Pikachu, then having each Pikachu choose a Pikachu. If the number of Pikachus carrying Pokeballs is finite, then eventually, this will demonstrate that the choice can be made and so the axiom of choice is unnecessary. However, if it's infinite, then this will generate a neverending stream of Pikachus. In the latter case, the game never begins, because you can't begin a Pokemon battle until all participants have chosen Pokemon. Most likely, the other players would simply abandon the game, which Cueball could claim as a victory. Hawthorn (talk) 13:52, 24 April 2015 (UTC)