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Lecture Notes for CMSC 250 - Discrete Structures with Plane at Maryland (UMD)

Notes Information

Material Type:Class Note
Professor:Plane
Class:CMSC 250 - Discrete Structures
Subject:Computer Science
University:University of Maryland
Term:Spring 2004
Keywords:
  • Inductive Step
  • Progression
  • Combinations
  • Geometric Progression
  • Negative Integers
  • Infinite Sets
  • Propositional
  • Transitivity
  • Strong Induction
  • Positive Integer
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Sample Document Text

1 Inductive Proofs Must Have . Base Case (value): - where you prove it is true about the base case . Inductive Hypothesis (value): - where you state what will be assume in this proof . Inductive Step (value): - show: . where you state what will be proven below - proof: . where you prove what is stated in the show portion . this proof must use the Inductive Hypothesis sometime during the proof Prove this statement: Base Case (n=1): Inductive Hypothesis (n=p): Inductive Step (n=p+1): Show: Proof:(in class)  = +=n i nni 1 2 )1(  = = 1 1 1 i i 1 2 2 2 )11(1 2 )1( ==+=+nn  = +=p i ppi 1 2 )1(  + = +++=1 1 2 )1)1)((1(p i ppi Variations . 2+4+6+8+.+20 = ?? . If you can use the fact: . Rearrange it into a form that works. . If you can't - you must prove it from scratch  = +=n i nni 1 2 )1( 2 Less Mathematical Example . If all we had was 2 and 5 cent coins, we could make any value greater than 3. . Base Case (n = 4): . Inductive Hypothesis...

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