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Warm-up Problem

Warm-up Problem. Prove by induction: Every n≥8 is the sum of 3’s and 5’s. Warm-up Problem. Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“ n is triquinqual ”). Warm-up Problem. Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“ n is triquinqual ”) Proof: n =.

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Warm-up Problem

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  1. Warm-up Problem Prove by induction: Every n≥8 is the sum of 3’s and 5’s

  2. Warm-up Problem Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”)

  3. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: • n =

  4. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: • n = 8 =

  5. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: • n = 8 = 3+5 is triquinqual • n = 9

  6. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9

  7. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9 = 3+3+3 is triquinqual • n =

  8. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9 = 3+3+3 is triquinqual • n = 10 = 5+5 is triquinqual • (I.H.) Assume

  9. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9 = 3+3+3 is triquinqual • n = 10 = 5+5 is triquinqual • (I.H.) Assume m ≥ 10 and every n≤m is triquinqual. Prove

  10. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9 = 3+3+3 is triquinqual • n = 10 = 5+5 is triquinqual • (I.H.) Assume m ≥ 10 and every n≤m is triquinqual. Prove m+1 is triquinqual.

  11. Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases • n = 8 = 3+5 is triquinqual • n = 9 = 3+3+3 is triquinqual • n = 10 = 5+5 is triquinqual • (I.H.) Assume m ≥ 10 and every n≤m is triquinqual. Prove m+1 is triquinqual. • m+1 is triquinqual because m+1 = (m-2)+3 and m-2 ≥ 8 is triquinqual.

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