Editing Talk:1516: Win by Induction

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. [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 13:52, 24 April 2015 (UTC)

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. [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 13:52, 24 April 2015 (UTC)

:I think you are confused about the AoC. AoC states that given any collection of elements, you can choose an element from EACH set. If you are choosing a pokemon from a collection of pokeballs, it's equivalent to choosing one full pokeball from the collection and you are picking an element from a single set, which doesn't involve the AoC (this is something you can always do as long as the set is non-empty). In the example in the comic, AoC is not needed because there is already a natural ordering (ignoring the alt-text, which would make the set a partial ordering), so it's trivial to construct a choice function for any subset (choose the "least" pikachu in the sequence). On the other hand, if we have infinite pikachus running wild, we would need the Axiom of Choice (preferably its equivalent, the Well-Ordering Theorem) to assert that they can be ordered so that all of them except one is captured in a pokeball held by another pikachu.[[User:Aube|Aube]] ([[User talk:Aube|talk]]) 05:10, 25 April 2015 (UTC)

:I think you are confused about the AoC. AoC states that given any collection of elements, you can choose an element from EACH set. If you are choosing a pokemon from a collection of pokeballs, it's equivalent to choosing one full pokeball from the collection and you are picking an element from a single set, which doesn't involve the AoC (this is something you can always do as long as the set is non-empty). In the example in the comic, AoC is not needed because there is already a natural ordering (ignoring the alt-text, which would make the set a partial ordering), so it's trivial to construct a choice function for any subset (choose the "least" pikachu in the sequence). On the other hand, if we have infinite pikachus running wild, we would need the Axiom of Choice (preferably its equivalent, the Well-Ordering Theorem) to assert that they can be ordered so that all of them except one is captured in a pokeball held by another pikachu.[[User:Aube|Aube]] ([[User talk:Aube|talk]]) 05:10, 25 April 2015 (UTC)

Why don't those Pikachu have tails? Have they been sliced off? Is this some kind of mutation?-🐼🐯😺🐱 {{unsigned|FlyingPiggy}}

Why don't those Pikachu have tails? Have they been sliced off? Is this some kind of mutation?-🐼🐯😺🐱 {{unsigned|FlyingPiggy}}