Abstract
This chapter discusses mathematical induction and recursion. Induction is a common proof technique in mathematics, and there are two parts to a proof by induction (the base case and the inductive step). We discuss strong and weak induction, and we discuss how recursion is used to define sets, sequences, and functions. This leads us to structural induction, which is used to prove properties of recursively defined structures.
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Notes
- 1.
This definition of mathematical induction covers the base case of n = 1 and would need to be adjusted if the number specified in the base case is higher.
- 2.
As before this definition covers the base case of n = 1 and would need to be adjusted if the number specified in the base case is higher.
- 3.
We are taking the Fibonacci sequence as starting at 1, whereas others take it as starting at 0.
- 4.
We will give an alternate definition of a tree in terms of a connected acyclic graph in Chap. 7 on graph theory.
Reference
Meyer B (1990) Introduction to the theory of programming languages. Prentice Hall
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O’Regan, G. (2023). Mathematical Induction and Recursion. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_6
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DOI: https://doi.org/10.1007/978-3-031-26212-8_6
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