Chapter 5: Q31E (page 371)
Is the recursive or the iterative algorithm for finding the sequence in Exercise 29 more efficient?
The iterative algorithm is used for finding the sequence.
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Let be the statement that in a triangulation of a simple polygon with sides, at least one of the triangles in the triangulation has two sides bordering the exterior of the polygon.
a) Explain where a proof using strong induction that is true for all integers runs into difficulties.
b) Show that we can prove that is true for all integers by proving by strong induction the stronger statement for all integers , which states that in every triangulation of a simple polygon, at least two of the triangles in the triangulation have two sides bordering the exterior of the polygon.
Prove that if h > - 1 , then for all nonnegative integers n. This is called Bernoulli’s inequality.
For which nonnegative integer’s n is Prove your answer.
Prove that a set with n elements has subsets containing exactly three elements whenever n is an integer greater than or equal to 3.
Prove that if and B are sets, then
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