lecture2 - CS245 Winter 2010 Lecture 2 Shai Ben-David Tools...

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Unformatted text preview: CS245 - Winter 2010, Lecture 2 Shai Ben-David Tools for precise definition of sets We wish to define formal languages that will enable precise treatment of logical notions (like validity and logical implication). The first step in the definition of a formal language is the definition of the set of legal ‘words’ (some times called ‘formulas’ or ‘sentences’) of that language. Let us begin our study by a discussion of tools by which such sets would be defined. How can we define sets precisely? There are several common methods for doing that: List of set members: the most straightforward method for defining a set is by listing all it elements. For example A = { 5 , 3 , 12 } or { John , Linda, Davis Center } . One major weakness of this method is that it cannot be used to define infinite sets. Description by a characterizing property: another common tool for defin- ing sets is by fixing some domain of elements and then specifying a prop- erty that is common to all members of that set and is not enjoyed by any domain element outside the defined set. For example, the set of even numbers is defined over the domain of natural numbers by E = { n : n is divisible by 2 } . Or, B = The set of all people with blue eyes ....
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This note was uploaded on 02/11/2010 for the course ART AFM101 taught by Professor Mr.lushman during the Spring '10 term at University of Toronto.

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lecture2 - CS245 Winter 2010 Lecture 2 Shai Ben-David Tools...

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