12.1. Discrete Mathematics

Try these first

1. 1.

   What is induction used for in mathematics?

   Hint

   Think about generalizing properties.

2. 2.

   State the two main components of proof by induction.

   Hint

   One proves the start and the other shows the next.

3. 3.

   What is the first step in a proof by induction?

   • Base Case
   • Inductive Step
   • Hypothesis

   Hint

   It's where you show the statement is true for the initial integer.

4. 4.

   Is the inductive step required to use all previous cases?

   • True
   • False

   Hint

   Think about how much information you can use.

5. 5.

   Formulate a proof using strong induction to show that every integer n ≥ 8 can be expressed as a sum of 3s and 5s.

   Hint

   Utilize previous integer sums effectively.

6. 6.

   Research and present an application of induction in real-world computational algorithms and discuss its significance.

   Hint

   Focus on algorithm properties and how induction validates them.