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Lecture Notes for MATH 125 - Discrete Mathematics I at George Mason (GMU)

Notes Information

Material Type:Class Note
Professor:Staff
Class:MATH 125 - Discrete Mathematics I
Subject:Mathematics
University:George Mason University
Term:--
Keywords:
  • Lecture Notes Math
  • Supplementary Lecture Notes
  • Ordered N-Tuples
  • Immediately
  • Possible Set
  • Observation
  • Continuous Data
  • Contradiction
  • Continued...
  • Propositional
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Supplementary Lecture Notes for Math 125-1 - Alexei V. Samsonovich 2/1/2007 6 Lecture 2: Sets, Relations and Functions A set S is a collection of distinct objects x 1 , x 2 , . called elements (or members) of the set. This is written as follows: S = {x 1 , x 2 , .}, and the expression x 1 ? S says that x 1 is a member of S (belongs to S). The notion of a set does not allow for multiple instances (repetitions) of the same element in the set, while the notion of a sequence (an ordered collection) does. The notion of a set does not relate to the notion of continuity, while at the same time it provides a basis for all concepts of continuous data structures (which are not a topic here). As far as the set theory per se is concerned, the nature of elements is irrelevant: all that matters is how many elements are and whether two elements x and y are one and the same element (x = y) or not (x ? y). For example, a set may contain another set (or even itself) as its element. A set ...

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