Discrrete mathematics for computer science strong induction warmup
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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:
on =
Warm-up Problem
• Prove by induction: Every n≥8 is the
sum of 3’s and 5’s (“n is triquinqual”)
• Proof:
on = 8 =
Warm-up Problem
• Prove by induction: Every n≥8 is the
sum of 3’s and 5’s (“n is triquinqual”)
• Proof:
o n = 8 = 3+5 is triquinqual
on = 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
o n = 8 = 3+5 is triquinqual
on = 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
o n = 8 = 3+5 is triquinqual
o n = 9 = 3+3+3 is triquinqual
on =
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
o n = 8 = 3+5 is triquinqual
o n = 9 = 3+3+3 is triquinqual
o n = 10 = 5+5 is triquinqual
o (I.H.) Assume
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
o n = 8 = 3+5 is triquinqual
o n = 9 = 3+3+3 is triquinqual
o n = 10 = 5+5 is triquinqual
o (I.H.) Assume m ≥ 10 and every n≤m is
triquinqual. Prove
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
o n = 8 = 3+5 is triquinqual
o n = 9 = 3+3+3 is triquinqual
o n = 10 = 5+5 is triquinqual
o (I.H.) Assume m ≥ 10 and every n≤m is
triquinqual. Prove m+1 is triquinqual.
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
o n = 8 = 3+5 is triquinqual
o n = 9 = 3+3+3 is triquinqual
o n = 10 = 5+5 is triquinqual
o (I.H.) Assume m ≥ 10 and every n≤m is
triquinqual. Prove m+1 is triquinqual.
o m+1 is triquinqual because m+1 = (m2)+3 and m-2 ≥ 8 is triquinqual.
