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| ====== Corpus Demonstratum: Collection of Proofs ====== | |
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| Welcome to our comprehensive collection of mathematical and philosophical proofs. This wiki aims to be a definitive resource for students, scholars, and enthusiasts seeking rigorous demonstrations across the spectrum of mathematical disciplines and philosophical traditions. | |
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| ===== About This Project ===== | |
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| This encyclopedia serves multiple purposes: | |
| * To collect and preserve important proofs in accessible formats | |
| * To provide clear explanations with appropriate levels of rigor | |
| * To highlight connections between different areas of mathematics and philosophy | |
| * To trace the historical development of key theorems and arguments | |
| * To serve as an educational resource for learners at various levels | |
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| ===== Getting Started ===== | |
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| * [[wiki:math|Mathematical expression formatting guide]] | |
| * [[templates:mathematical|Mathematical proof template]] | |
| * [[templates:philosophical|Philosophical argument template]] | |
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| ===== Mathematical Proofs ===== | |
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| ==== Foundations of Mathematics ==== | |
| * [[start:proofs:foundations:logic|Logic and Set Theory]] | |
| * [[start:proofs:foundations:logic:incompleteness|Gödel's Incompleteness Theorems]] | |
| * [[start:proofs:foundations:logic:compactness|Compactness Theorem]] | |
| * [[start:proofs:foundations:logic:completeness|Completeness Theorem]] | |
| * [[start:proofs:foundations:logic:zfc|ZFC Axioms and Consequences]] | |
| * [[start:proofs:foundations:logic:choice|Axiom of Choice and Equivalents]] | |
| * [[start:proofs:foundations:numbers|Number Systems]] | |
| * [[start:proofs:foundations:numbers:peano|Peano Axioms]] | |
| * [[start:proofs:foundations:numbers:integers|Construction of Integers]] | |
| * [[start:proofs:foundations:numbers:rationals|Construction of Rational Numbers]] | |
| * [[start:proofs:foundations:numbers:reals|Construction of Real Numbers]] | |
| * [[start:proofs:foundations:numbers:complex|Complex Numbers]] | |
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| ==== Number Theory ==== | |
| * [[start:proofs:number:elementary|Elementary Number Theory]] | |
| * [[start:proofs:number:elementary:division|Division Algorithm]] | |
| * [[start:proofs:number:elementary:euclidean|Euclidean Algorithm]] | |
| * [[start:proofs:number:elementary:fundamental|Fundamental Theorem of Arithmetic]] | |
| * [[start:proofs:number:elementary:fermat|Fermat's Little Theorem]] | |
| * [[start:proofs:number:elementary:euler|Euler's Theorem]] | |
| * [[start:proofs:number:analytic|Analytic Number Theory]] | |
| * [[start:proofs:number:analytic:pnt|Prime Number Theorem]] | |
| * [[start:proofs:number:analytic:dirichlet|Dirichlet's Theorem on Primes]] | |
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| ==== Algebra ==== | |
| * [[start:proofs:algebra:group|Group Theory]] | |
| * [[start:proofs:algebra:group:lagrange|Lagrange's Theorem]] | |
| * [[start:proofs:algebra:group:sylow|Sylow Theorems]] | |
| * [[start:proofs:algebra:group:isomorphism|Isomorphism Theorems]] | |
| * [[start:proofs:algebra:ring|Ring Theory]] | |
| * [[start:proofs:algebra:ring:ideals|Ideal Theory]] | |
| * [[start:proofs:algebra:ring:ufd|Unique Factorization Domains]] | |
| * [[start:proofs:algebra:field|Field Theory]] | |
| * [[start:proofs:algebra:field:extensions|Field Extensions]] | |
| * [[start:proofs:algebra:field:splitting|Splitting Fields]] | |
| * [[start:proofs:algebra:galois|Galois Theory]] | |
| * [[start:proofs:algebra:galois:fundamental|Fundamental Theorem of Galois Theory]] | |
| * [[start:proofs:algebra:galois:solvability|Solvability by Radicals]] | |
| * [[start:proofs:algebra:linear|Linear Algebra]] | |
| * [[start:proofs:algebra:linear:determinants|Determinants]] | |
| * [[start:proofs:algebra:linear:eigenvalues|Eigenvalues and Eigenvectors]] | |
| * [[start:proofs:algebra:linear:diagonalization|Diagonalization]] | |
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| ==== Analysis ==== | |
| * [[start:proofs:analysis:calculus|Calculus]] | |
| * [[start:proofs:analysis:calculus:limits|Limit Theorems]] | |
| * [[start:proofs:analysis:calculus:mvt|Mean Value Theorem]] | |
| * [[start:proofs:analysis:calculus:fundamental|Fundamental Theorem of Calculus]] | |
| * [[start:proofs:analysis:real|Real Analysis]] | |
| * [[start:proofs:analysis:real:sequences|Convergence of Sequences]] | |
| * [[start:proofs:analysis:real:series|Convergence of Series]] | |
| * [[start:proofs:analysis:real:riemann|Riemann Integration]] | |
| * [[start:proofs:analysis:real:lebesgue|Lebesgue Integration]] | |
| * [[start:proofs:analysis:complex|Complex Analysis]] | |
| * [[start:proofs:analysis:complex:cauchy|Cauchy's Integral Theorem]] | |
| * [[start:proofs:analysis:complex:residue|Residue Theorem]] | |
| * [[start:proofs:analysis:complex:laurent|Laurent Series]] | |
| * [[start:proofs:analysis:functional|Functional Analysis]] | |
| * [[start:proofs:analysis:functional:baire|Baire Category Theorem]] | |
| * [[start:proofs:analysis:functional:hahn-banach|Hahn-Banach Theorem]] | |
| * [[start:proofs:analysis:functional:spectral|Spectral Theory]] | |
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| ==== Geometry and Topology ==== | |
| * [[start:proofs:geometry:euclidean|Euclidean Geometry]] | |
| * [[start:proofs:geometry:euclidean:pythagoras|Pythagorean Theorem]] | |
| * [[start:proofs:geometry:euclidean:congruence|Triangle Congruence Theorems]] | |
| * [[start:proofs:geometry:euclidean:similarity|Similar Triangles]] | |
| * [[start:proofs:geometry:differential|Differential Geometry]] | |
| * [[start:proofs:geometry:differential:curves|Theory of Curves]] | |
| * [[start:proofs:geometry:differential:surfaces|Theory of Surfaces]] | |
| * [[start:proofs:geometry:differential:manifolds|Manifolds]] | |
| * [[start:proofs:topology:point-set|Point-Set Topology]] | |
| * [[start:proofs:topology:point-set:metric|Metric Spaces]] | |
| * [[start:proofs:topology:point-set:continuity|Continuous Functions]] | |
| * [[start:proofs:topology:point-set:compactness|Compactness]] | |
| * [[start:proofs:topology:algebraic|Algebraic Topology]] | |
| * [[start:proofs:topology:algebraic:fundamental|Fundamental Group]] | |
| * [[start:proofs:topology:algebraic:homology|Homology Groups]] | |
| * [[start:proofs:topology:algebraic:fixed-point|Fixed Point Theorems]] | |
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| ==== Applied Mathematics ==== | |
| * [[start:proofs:applied:probability|Probability Theory]] | |
| * [[start:proofs:applied:probability:axioms|Kolmogorov Axioms]] | |
| * [[start:proofs:applied:probability:distributions|Probability Distributions]] | |
| * [[start:proofs:applied:probability:limit|Limit Theorems]] | |
| * [[start:proofs:applied:differential|Differential Equations]] | |
| * [[start:proofs:applied:differential:first-order|First-Order ODEs]] | |
| * [[start:proofs:applied:differential:linear|Linear ODEs]] | |
| * [[start:proofs:applied:differential:pde|Partial Differential Equations]] | |
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| ==== Famous Theorems and Problems ==== | |
| * [[start:proofs:famous:fermat|Fermat's Last Theorem]] | |
| * [[start:proofs:famous:four-color|Four Color Theorem]] | |
| * [[start:proofs:famous:poincare|Poincaré Conjecture]] | |
| * [[start:proofs:famous:riemann|Riemann Hypothesis]] | |
| * [[start:proofs:famous:p-np|P vs NP Problem]] | |
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| ===== Philosophical Arguments and Proofs ===== | |
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| ==== Metaphysics ==== | |
| * [[start:proofs:philosophy:metaphysics:ontology|Ontological Arguments]] | |
| * [[start:proofs:philosophy:metaphysics:ontology:anselm|Anselm's Ontological Argument]] | |
| * [[start:proofs:philosophy:metaphysics:ontology:descartes|Descartes' Ontological Argument]] | |
| * [[start:proofs:philosophy:metaphysics:ontology:modal|Modal Ontological Arguments]] | |
| * [[start:proofs:philosophy:metaphysics:causation|Causation]] | |
| * [[start:proofs:philosophy:metaphysics:causation:cosmological|Cosmological Arguments]] | |
| * [[start:proofs:philosophy:metaphysics:causation:kalam|Kalam Cosmological Argument]] | |
| * [[start:proofs:philosophy:metaphysics:causation:regress|Infinite Regress Arguments]] | |
| * [[start:proofs:philosophy:metaphysics:mind|Philosophy of Mind]] | |
| * [[start:proofs:philosophy:metaphysics:mind:dualism|Arguments for Dualism]] | |
| * [[start:proofs:philosophy:metaphysics:mind:physicalism|Arguments for Physicalism]] | |
| * [[start:proofs:philosophy:metaphysics:mind:mary|Knowledge Argument (Mary's Room)]] | |
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| ==== Epistemology ==== | |
| * [[start:proofs:philosophy:epistemology:knowledge|Nature of Knowledge]] | |
| * [[start:proofs:philosophy:epistemology:knowledge:jtb|Knowledge as Justified True Belief]] | |
| * [[start:proofs:philosophy:epistemology:knowledge:gettier|Gettier Problems]] | |
| * [[start:proofs:philosophy:epistemology:knowledge:reliabilism|Reliabilist Theories]] | |
| * [[start:proofs:philosophy:epistemology:skepticism|Skeptical Arguments]] | |
| * [[start:proofs:philosophy:epistemology:skepticism:vat|Brain in a Vat]] | |
| * [[start:proofs:philosophy:epistemology:skepticism:demon|Descartes' Evil Demon]] | |
| * [[start:proofs:philosophy:epistemology:skepticism:dream|Dream Argument]] | |
| * [[start:proofs:philosophy:epistemology:induction|Problem of Induction]] | |
| * [[start:proofs:philosophy:epistemology:induction:hume|Hume's Problem of Induction]] | |
| * [[start:proofs:philosophy:epistemology:induction:goodman|Goodman's New Riddle of Induction]] | |
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| ==== Ethics ==== | |
| * [[start:proofs:philosophy:ethics:normative|Normative Ethics]] | |
| * [[start:proofs:philosophy:ethics:normative:utilitarian|Utilitarian Arguments]] | |
| * [[start:proofs:philosophy:ethics:normative:kantian|Kantian Arguments]] | |
| * [[start:proofs:philosophy:ethics:normative:virtue|Virtue Ethics]] | |
| * [[start:proofs:philosophy:ethics:metaethics|Metaethics]] | |
| * [[start:proofs:philosophy:ethics:metaethics:realism|Moral Realism]] | |
| * [[start:proofs:philosophy:ethics:metaethics:error|Error Theory]] | |
| * [[start:proofs:philosophy:ethics:metaethics:emotivism|Emotivism]] | |
| * [[start:proofs:philosophy:ethics:applied|Applied Ethics]] | |
| * [[start:proofs:philosophy:ethics:applied:trolley|Trolley Problem]] | |
| * [[start:proofs:philosophy:ethics:applied:value|Value of Life Arguments]] | |
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| ==== Logic and Language ==== | |
| * [[start:proofs:philosophy:logic:formal|Formal Logic]] | |
| * [[start:proofs:philosophy:logic:formal:propositional|Propositional Logic]] | |
| * [[start:proofs:philosophy:logic:formal:predicate|Predicate Logic]] | |
| * [[start:proofs:philosophy:logic:formal:modal|Modal Logic]] | |
| * [[start:proofs:philosophy:logic:informal|Informal Logic and Fallacies]] | |
| * [[start:proofs:philosophy:logic:informal:deductive|Deductive Fallacies]] | |
| * [[start:proofs:philosophy:logic:informal:inductive|Inductive Fallacies]] | |
| * [[start:proofs:philosophy:language:meaning|Theories of Meaning]] | |
| * [[start:proofs:philosophy:language:meaning:reference|Reference Theories]] | |
| * [[start:proofs:philosophy:language:meaning:use|Use Theories]] | |
| * [[start:proofs:philosophy:language:meaning:verification|Verification Principle]] | |
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| ==== Philosophy of Science ==== | |
| * [[start:proofs:philosophy:science:demarcation|Demarcation Problem]] | |
| * [[start:proofs:philosophy:science:demarcation:popper|Popper's Falsificationism]] | |
| * [[start:proofs:philosophy:science:demarcation:kuhn|Kuhn's Paradigm Shifts]] | |
| * [[start:proofs:philosophy:science:explanation|Scientific Explanation]] | |
| * [[start:proofs:philosophy:science:explanation:dn|Deductive-Nomological Model]] | |
| * [[start:proofs:philosophy:science:explanation:causal|Causal Accounts]] | |
| * [[start:proofs:philosophy:science:realism|Scientific Realism vs. Anti-Realism]] | |
| * [[start:proofs:philosophy:science:realism:miracles|No Miracles Argument]] | |
| * [[start:proofs:philosophy:science:realism:pessimistic|Pessimistic Induction]] | |
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| ===== How to Contribute ===== | |
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| We welcome contributions from mathematicians, philosophers, educators, and enthusiasts. To contribute: | |
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| * **Follow our standards**: Use the proper templates for consistency | |
| * **Use proper notation**: Ensure mathematical expressions use LaTeX via the MathJax plugin | |
| * **Provide references**: Include sources for all theorems, proofs, and arguments | |
| * **Consider accessibility**: Write clear explanations that build on prerequisites | |
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| ===== Contact ===== | |
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| For questions or assistance with this wiki, please contact [[mailto:ayman@aymanlafaz.com|ayman@aymanlafaz.com]]. | |
