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text: '## Learning the Axiom of Choice ##\n\n[multiple-choice(q_level_of_math_logic): What do you know about set theory, mathematical logic and axiom systems?\na: Almost nothing\nwants: [axiom_of_choice_definition_intutive] [axiom_of_choice_finite_sets] [banach_tarski_paradox] [axiom_of_choice_function_existence] [axiom_of_choice_how_can_something_be_neither_true_nor_false]\n-wants: [6c8]\nb: Well, I've used them for other maths, but haven't studied them directly.\nwants: [axiom_of_choice_definition_intutive] [axiom_of_choice_finite_sets] [axiom_of_choice_function_existence] [axiom_of_choice_how_can_something_be_neither_true_nor_false]\n-wants: [6c8] [banach_tarski_paradox]\nc: I have a good grasp of it, but would like some explanation anyway. \nwants: [6c8] [axiom_of_choice_finite_sets] [axiom_of_choice_function_existence] [axiom_of_choice_how_can_something_be_neither_true_nor_false]\n-wants: [6cb] [banach_tarski_paradox]\nd: I have a good grasp of it and don't need to hear more. \nwants: [6c8] \n-wants: [6cb] [axiom_of_choice_finite_sets] [axiom_of_choice_function_existence] [banach_tarski_paradox][axiom_of_choice_how_can_something_be_neither_true_nor_false]\n]\n\n\n[multiple-choice(q_axiom_of_choice_history): This axiom has a rich and interesting history. How much do you want to learn about? \na: Give me all of the juicy history side-facts!\nwants: [6c7] [6c9]\nb: Eh, give me a short intro.\nwants: [6c7]\n-wants: [6c9]\nc: Just stick to the mathematics, please.\n-wants: [6c7] [6c9]\n]\n\n\n[multiple-choice(q_axiom_of_choice_history): This axiom has a rich and interesting history. How much do you want to learn about? \na: Give me all of the juicy history side-facts!\nwants: [6c7] [6c9]\nb: Eh, give me a short intro.\nwants: [6c7]\n-wants: [6c9]\nc: Just stick to the mathematics, please.\n-wants: [6c7] [6c9]\n]\n\n[multiple-choice(q_axiom_of_choice_mathematics): How heavy should the maths be that we show you? \na: Lay it on me! Give me the formal logical notation.\nwants: [6c8]\n-wants: [6cb]\nb: Just give me an intuitive description with words. No mathematical notation.\n-wants: [6c8]\nwants: [6cb]\n]\n\n%%%box:\nYou will get the following pages:\n%%wants-requisite([6c7]):\nBasic intro %%\n%%wants-requisite([6c9]):\nHistory and controversy %%\n%%wants-requisite([6c8]):\nDefinition (Formal) %%\n%%wants-requisite([6c7]):\nDefinition (Intuitive) %%\n%%wants-requisite([6cb]):\n\n%start-path([6c9])%\n%%\n%%%\n\n\n\n\nPlan for this guide:\n\nAxiom of Choice: Guide\n\n\n\nConditional paragraphs for concepts being described on later pages.\n\nQuestions on what the main page should look like\n\n1 Introduction\n2 Getting the Heavy Maths out the Way: Definitions\n3 Axiom Unnecessary for Finite Collections of Sets\n4 Controversy: Mathematicians Divided! Counter-Intuitive Results, and The History of the Axiom of Choice\n5 So, What is this Choice Thing Good for Anyways?\n6 Physicists Hate Them! Find out How Banach and Tarski Make Infinity Dollars with this One Simple Trick!\n7 How Something Can Exist Without Actually Existing: The Zermelo Fraenkel Axioms and the Existence of a Choice Function\n8 How Something can be Neither True nor False:\n9 A Rose by Any Other Name: Alternative Characterizations of AC\n10 Zorn's Lemma? I hardly Know her!\n11 Getting Your Ducks in a Row, or, Rather, Getting Your Real Numbers in a Row: The Well-Ordering Principle\n12 AC On a Budget: Weaker Versions of the Axiom\n13 And In Related News: The Continuum Hypothesis\n14 Axiom of Choice Considered Harmful: Constructive Mathematics and the Potential Pitfalls of AC\n15 Choosing Not to Choose: Set-Theoretic Axioms Which Contradict Choice\n16 I Want to Play a Game: Counterintuitive Strategies Using AC \n\n-Guide Questions-\n\nI'd also like the corresponding pages to show or hide some information based on what is chosen here. \n\nChoose one of the pregenerated paths, or customize your own.\na. Comprehensive path: Learn more than you wanted to know!\n\tAdd all pages\nb. Substantial path: All the most important stuff\n\tAdd 1,2,3,4,5,6,7,8,10,14\nc. Compact path: Only the very important stuff\n\tAdd 2, 3, 5, 7, 10\nd. First-time path: Learn the important basics without getting too bogged down.\n\tAdd 1. 2 (intuitive), 2 (definition), 3, 4, 5, 6, 7, 8, 10\ne. Overview path: Just get a taste of the axiom\n\tAdd 1, 2 (intuitive), 2 (definition), 3, 4, 5, 7\nf. Custom Path\n\n\n\nIf the user chooses to customize a path:\n1. What do you know about set theory, mathematical logic and axioms?\na. Almost nothing\n\tAdd Definitions (Intuitive)\n\tAdd 3. Finite Sets\n\tAdd 6. Banach-Tarski\n\tAdd 7. ZF Axioms and Existence of a Choice Function\n\tAdd 8. How can something be neither True nor False\nb. Well, I've used them for other maths, but haven't studied them directly.\n\tAdd 2. Definitions\t\n\tAdd 3. Finite Sets\n\tAdd 7. ZF Axioms and Existence of a Choice Function\n\tAdd 8. How can something be neither True nor False\nc. I have a good grasp of it, but would like some explanation anyway. \n\tAdd 2. Definitions\n\tAdd 3. Finite Sets\n\tAdd 7. ZF Axioms and Existence of a Choice Function\n\tAdd 8. How can something be neither True nor False\nd. I have a good grasp of it and don't need to hear more. \n\tAdd 2. Definitions\n\n\n2. This axiom has a rich and interesting history. How much do you want to learn about?\na. Give me all of the juicy history side-facts!\n\tAdds 1. Introduction\n\tAdds 4. Controversy (History)\nb. Eh, give me a short intro.\n\tAdds 1. Intro\nc. Just stick to the mathematics, please.\n\n\n-Questions 3-5 are revealed if, and only if, the answer to Question 1 is b,c, or d.-\n\n32. How much detail would you like to read about the mathematics related to the axiom?\na. I'd like to know a lot of the detail.\n\tAdds 5. What is this Choice Thing Good For\n\tAdds 9. Alternative Characterizations\n\tAdds 10. Zorn's Lemma\n\tAdds 12. Weaker Versions of the Axiom\n\tAdds 13. Continuum Hypthesis\nb. I only want the most important extra details.\n\tAdds 5. What is this Choice thing good for\n\tAdds 10. Zorn's Lemma\nc. I only want the absolute essentials.\n\n4. How much would you like to know about constructive mathematics and its relation to the axiom of choice?\na. I don't care to read about it right now.\nb. I don't know what that is, please tell me about it.\n\tAdds 14. Constructive Mathematics and Pitfalls of AC\n\tPotentially adds a link to an intro on constructivsm.\nc. I know what it is, but I would like to hear more about how it relates to Axiom of Choice.\n\tAdds 14. Constructive Mathematics and Pitfalls of AC\n5. How much do you care about the paradoxes the axiom implies? \na. I don't care about them, I just want to know about the axiom itself.\nb. Give me a very basic overview.\n\tAdds 6. Banach-Tarski Paradox\nd. Just tell me some interesting ones.\n\tAdds 6. Banach-Tarksi Paradox\n\tAdds 16. Counterintuitive strategies using AC\nc. Tell me the whole story! \n\tAdds 6. Banach-Tarski Paradox\n\tAdds 11. Well-Ordering Principle\n\tAdds 15. Axioms which contradict choice\n\tAdds 16. Counterintuitive strategies using AC\n\n\n\n\nO',
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