Homework 4

For the week of Sept. 28-Oct. 2.
  1. Exercises 3.7 and 3.9.
  2. Exercise 3.27
  3. Exercise 3.41
  4. Exercise 3.43
  5. Recall that for any real number x, the floor of x, written ⌊x⌋, is defined to be the greatest integer less than or equal to x. Prove by induction that for all natural numbers n, ⌊n/2⌋ = n/2 if n is even, and ⌊n/2⌋ = (n-1)/2 if n is odd.