# 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 StepProgressionCombinationsGeometric ProgressionNegative IntegersInfinite SetsPropositionalTransitivityStrong InductionPositive Integer

## 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...

## Related Documents

Inductive Step Notes
Inductive Step Notes
Mathematical Induction Notes
Square Brackets Quiz
Provided That Quiz
Progression Quiz
Combinations Exam
Best Wishes Notes
Square Brackets Quiz
Cmsc 250 Quiz Quiz
Combinations Exam