14.1.4. Question Number 9

Try these first

1. 1.

   Explain what a power of two is and give three examples.

   Hint

   Remember the pattern: 2 raised to increasing integers.

2. 2.

   What does the base case in induction typically represent?

   Hint

   Think about starting points in proof.

3. 3.

   What does mathematical induction help to establish?

   • Prove equations
   • Establish truths for positive integers
   • Summarize theories

   Hint

   Look at concepts we've discussed regarding integers.

4. 4.

   True or False: The base case is always proven for n = 0.

   • True
   • False

   Hint

   Reflect on our starting points in proofs.

5. 5.

   If given a number N = 23, express it using distinct powers of two and show the reasoning.

   Hint

   Break it down using binary representation techniques.

6. 6.

   How could we represent the number 30 using distinct powers of two? Explain your process.

   Hint

   Consider what makes each number 'even' or 'distinctly combined.'