In mathematics, induction is a method of proving the validity of a statement asserting that all cases must be true provided the first case was true. Learn how the uses and proofs of mathematical induction can determine the validity of a mathematical statement. ...
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Lehet E (2021a) Induction and explanatory definitions in mathematics. Synthese 198(2):1161–1175 Article Google Scholar Lehet E (2021b) Mathematical Explanation in Practice. Axiomathes 31(5):553–574 Article Google Scholar Liebeck W (2008) The insolubility of the quintic. In: Gowers T, ...
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Ch 2. Mathematic Inductions Ch 3. Types of Proofs in Math Ch 4. Numerical Problem Solving Skills Ch 5. Principles of Mathematical Sets Ch 6. Groups & Sets in Algebra Ch 7. Number Theory Overview Ch 8. Rational & Irrational Numbers Overview ...
Let us consider the following two questions: 1. What is the relationship between the logical foundations of mathematical reasoning and the actual practice of mathematicians? 2. In what ways can computers support the development and communication of mathematical knowledge? 1a Logical Foundations Our firs...
Let us consider the following two questions: 1. What is the relationship between the logical foundations ofmathematical reasoningand the actual practice of mathematicians? 2. In what ways can computers support the development and communication ofmathematical knowledge?
guided by questions such as, “What mathematical knowledge matters for effective teaching and does it impact students’ mathematical achievement?”. The focus on the actual work of teaching was linked to the intention to increase the relevance of the identified knowledge to practice and to focus on...
The first part of the discussion served to establish some com- mon ground for myself as the teacher and the students as class members, enabling them as a group to go on to new questions about exponents. Conscious Guessing and Proof That Zig-Zags Between Induction and Deduction After this ...
10. In the case of investigations directed at the solution of specific questions or problems, Detlefsen and Arana speak of “directed investigations” (Detlefsen and Arana2011, 9); see also the notion of a “trial” in a mathematical thought experiment (Starikova and Giaquinto2018, 263). ...