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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:Fall 2006
Keywords:
  • Contrapositive
  • Definitions
  • Contradiction
  • Interpretation
  • Infinite Sets
  • Propositional
  • Contraposition
  • Positive Integers
  • Counter Example
  • Infinite Number
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Sample Document Text

Proof Must Have . Statement of what is to be proven. . "Proof:" to indicate where the proof starts . Clear indication of flow . Clear indication of reason for each step . Careful notation, completeness and order . Clear indication of the conclusion . I suggest pencil and good erasure when needed Number Theory - Ch 3 Definitions . Z --- integers . Q - rational numbers (quotients of integers) -r?Q ??a,b?Z, (r = a/b) ^ (b ? 0) . Irrational = not rational . R --- real numbers . superscript of + --- positive portion only . superscript of - --- negative portion only . other superscripts: Z even , Z odd , Q >5 . "closure" of these sets for an operation - Z closed under what operations? Integer Definitions . even integer -n ?Z even ??k ? Z, n = 2k . odd integer -n ? Z odd ??k ? Z, n = 2k+1 . prime integer (Z >1 ) -n ?Z prime ??r,s?Z + , (n=r*s) ?(r=1)v(s=1) . composite integer (Z >1 ) -n ? Z composite ??r,s?Z + , n=r*s ^(r?1)^(s?1) Constructive...

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