mathematical induction

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mathematical induction

n.
Induction.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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From these assumptions and previously established results, the desired result may be deduced through an application of formal logic (proof by induction is an exception).
He begins by picking up discrete calculus, including proof by induction, and moves to selected area computation (pi, anyone?), limit's and Taylor's theorem, including series representations and Taylor polynomials, infinite series, including both the positive and the general, beginning logic, including propositional logic, predicates and quantifiers, and proofs, real numbers, functions such as derivatives and a substantial pair of chapters on integrals.
I illustrate a student in real analysis who followed this learning progression to learn the concept of proof by induction. Finally, I note that many students who view proof as a process fail to ever view proof as an argument and I discuss the consequences of these students' narrow view of proof.