Journal ArticleDOI
Using Continuity Induction
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In this article, a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction pass, is presented.Abstract:
Here is a technique for proving the fundamental theorems of analysis that provides a unified way to pass from local properties to global properties on the real line, just as ordinary induction pass...read more
Citations
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Journal ArticleDOI
The Instructor’s Guide to Real Induction
TL;DR: Real induction is introduced, a proof technique analogous to Mathematical Induction but applicable to statements indexed by an interval on the real line, and inductive principles in arbitrary ordered sets are pursued.
Posted Content
Putting OPEC Out of Business
TL;DR: In this article, the authors explain the recent peak and subsequent collapse in oil prices by strategic interaction between a limit-pricing oil cartel and an importer producing substitutes to oil, with productin costs falling with R&D investment.
Book ChapterDOI
A local-global principle for the real continuum
TL;DR: The aim is to improve the set of available tools in real analysis, where the local-global principle is used as a unifying principle from which the other completeness axioms and several classical theorems are proved in a fairly direct way.
Posted Content
Characterizing Positively Invariant Sets: Inductive and Topological Methods.
Khalil Ghorbal,Andrew Sogokon +1 more
TL;DR: This article contributes an explicit development of modern methods for checking positively invariant sets of ordinary differential equations and describes two possible characterizations of positive invariants: one based on the real induction principle, and a novel alternative based on topological notions.
Journal ArticleDOI
First-Order Continuous Induction and a Logical Study of Real Closed Fields
Saeed Salehi,Mohammadsaleh Zarza +1 more
TL;DR: In this paper, the authors show that one of the three forms of continuous induction is weaker than the other two by proving that it is equivalent to the Archimedean property, while the other stronger versions are equivalent to completeness property of the real numbers.
References
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Book ChapterDOI
Induction over the Continuum
TL;DR: The analogy between the well ordering principle for nonempty subsets of N (the set of natural numbers) and the existence of a greatest lower bound for non-empty subset of [a,b] is exploited to formulate a principle of induction over the continuum for [ a,b) analogous to induction over N.
Journal ArticleDOI
Mathematical Induction in Sets
TL;DR: In this article, the inductive induction in sets problem was studied in the context of sets and inductive induction in sets, and the results showed that it is NP-hard.
BookDOI
Induction, Algorithmic Learning Theory, and Philosophy
TL;DR: This is the first book to collect essays from philosophers, mathematicians and computer scientists working at the exciting interface of algorithmic learning theory and the epistemology of science and inductive inference to provide engaging surveys of different, complementary, and mutually inspiring approaches to the topic.