In intuitionistic type theory (ITT), a discipline within mathematical logic, induction-recursion is a feature for simultaneously declaring a type and function on that type. It allows the creation of larger types, such as universes, than inductive types. The types created still remain predicative inside ITT. An inductive definition is given by rules for generating elements of a type. One can then define functions from that type by induction on the way the elements of the type are generated. Induction-recursion generalizes this situation since one can simultaneously define the type and the function, because the rules for generating elements of the type are allowed to refer to the function. Induction-recursion can be used to define large types including various universe constructions. It increases the proof-theoretic strength of type theory substantially. Nevertheless, inductive-recursive recursive definitions are still considered predicative. (Wikipedia).
Second Order Recurrence Formula (1 of 3: Prologue - considering the old course)
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From playlist Further Proof by Mathematical Induction
Induction, bijections, products -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Sequences: Introduction to Solving Recurrence Relations
This video introduces solving recurrence relations by the methods of inspection, telescoping, and characteristic root technique. mathispower4u.com
From playlist Sequences (Discrete Math)
Get the Code: http://goo.gl/S8GBL Welcome to my Java Recursion tutorial. In this video, I'm going to cover java recursion in 5 different ways. I figured if I show it using many different diagrams that it will make complete sense. A recursive method is just a method that calls itself. As
From playlist Java Algorithms
Applying the recursive formula to a sequence to determine the first five terms
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From playlist Sequences
How to use the recursive formula to evaluate the first five terms
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From playlist Sequences
The foundation -- Number Theory 1
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From playlist Number Theory v2
Peano Arithmetic -- Number Theory 1
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From playlist Number Theory
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From playlist Haskell - Functional Programming Fundamentals (Dr. Erik Meijer )
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From playlist Discrete Math I (Entire Course)
Discrete Math II - 5.3.2 Structural Induction
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From playlist Discrete Math II/Combinatorics (entire course)
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From playlist Principle of Mathematical Induction
Foundations - Seminar 14 - Gödel's incompleteness theorem Part 6
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From playlist Foundations seminar
C9 Lectures: Dr. Erik Meijer - Functional Programming Fundamentals Chapter 6 of 13
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From playlist Haskell - Functional Programming Fundamentals (Dr. Erik Meijer )
1.10.7 Recursive Functions: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015
Introduction to the Coq Proof Assistant - Andrew Appel
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From playlist Mathematics
How to determine the first five terms for a recursive sequence
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From playlist Sequences