# 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: Fall 2006 Keywords: Inductive StepProgressionCombinationsGeometric ProgressionNegative IntegersInfinite SetsPropositionalTransitivityStrong InductionPositive Integer      ## Sample Document Text

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 in the next section -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 nn i 1 2 )1( ? = = 1 1 1 i i 1 2 2 2 )11(1 2 )1( == + = +nn ? = + = p i pp i 1 2 )1( ? + = +++ = 1 1 2 )1)1)((1( p i pp i 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 nn i 1 2 )1( Less Mathematical Example . If all we had was 2 and 5 cent coins, we could make any value greater than 3. ...

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