Editing Talk:1516: Win by Induction
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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). | 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 | + | 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 [i]infinitely many[/i] 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. [[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) | ||
