Abstract
Mathematical induction Mathematical induction is an important proof technique used in mathematics, and it is often used to establish the truth of a statement for all natural numbers. There are two parts to a proof by induction, and these are the base step and the inductive step.
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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. 9 on graph theory.
Reference
Introduction to the Theory of Programming Languages. Bertrand Meyer. Prentice Hall. 1990.
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O’Regan, G. (2016). Mathematical Induction and Recursion. In: Guide to Discrete Mathematics. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44561-8_4
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DOI: https://doi.org/10.1007/978-3-319-44561-8_4
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