Mathematical Induction
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Home > Art, Film & Photography > Mathematical Induction: Wellfoundedness, Well-Order, Transfinite Induction, Axiom of Regularity, Ascending Chain Condition
Mathematical Induction: Wellfoundedness, Well-Order, Transfinite Induction, Axiom of Regularity, Ascending Chain Condition

Mathematical Induction: Wellfoundedness, Well-Order, Transfinite Induction, Axiom of Regularity, Ascending Chain Condition


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Wellfoundedness, Well-order, Transfinite induction, Axiom of regularity, Ascending chain condition, Infinite descending chain, Well-ordering principle, Konig's lemma, Robertson-Seymour theorem, Scott-Potter set theory, Well-quasi-ordering, Well-founded relation, Structural induction, Kruskal's tree theorem, Non-well-founded set theory, Universal set, Prewellordering, Mostowski collapse lemma, Noetherian topological space, Axiom of limitation of size, Coinduction, Newman's lemma, Bar induction, Higman's lemma, Epsilon-induction. Excerpt: Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive integers). It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one. The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning. In 370 BC, Plato's Parmenides may have contained an early example of an implicit inductive proof. The earliest implicit traces of mathematical induction can be found in Euclid's proof that the number of primes is infinite and in Bhaskara's "cyclic method." An opposite iterated technique, counting down rather than up, is found in the Sorites paradox, where one argued that if 1,000,000 g...


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Product Details
  • ISBN-13: 9781234589288
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Weight: 68 gr
  • ISBN-10: 1234589281
  • Publisher Date: 08 Oct 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Wellfoundedness, Well-Order, Transfinite Induction, Axiom of Regularity, Ascending Chain Condition
  • Width: 189 mm


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