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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/02%3A__Induction_and_RecursionThe principle of mathematical induction states that In order to prove a statement about an integer n, if we can 1. Prove the statement when n = b, for some fixed integer b, and 2. Show that the truth ...The principle of mathematical induction states that In order to prove a statement about an integer n, if we can 1. Prove the statement when n = b, for some fixed integer b, and 2. Show that the truth of the statement for n = k − 1 implies the truth of the statement for n = k whenever k > b, then we can conclude the statement is true for all integers n ≥ b.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/04%3A_Mathematical_Induction/4.03%3A_Induction_and_RecursionIn a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can t...In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can think of a sequence as an infinite list of numbers that are indexed by the natural numbers. Another way to define a sequence is to give a specific definition of the first term and then state how to determine the next term in terms of previous terms; this process is known as definition by recursion.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/04%3A_Mathematical_Induction/4.03%3A_Induction_and_RecursionIn a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can t...In a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use this same idea to define a sequence as well. We can think of a sequence as an infinite list of numbers that are indexed by the natural numbers. Another way to define a sequence is to give a specific definition of the first term and then state how to determine the next term in terms of previous terms; this process is known as definition by recursion.
