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set theory

# set theory - Introduction Set theory is fundamental to...

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8/22/2007 1 LING 178 Introduction Set theory is fundamental to mathematics and has a number of direct applications in linguistics. We start by characterizing briefly the most important concepts in the field of set theory. Set (definition) A set is a group of objects represented as a unit. A set may contain any type of object, numbers, words, drawings, etc. they are called the members (or elements ) of the set . Sets are referred to with CAPITAL letters (the set A). Members of a set in lower-case (a is a member of A). Examples of sets … 34 12 119 98 65 1 Set A Set B Set C terrible tortoise tundra tiddlywink

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8/22/2007 2 Beware! There is a difference between x and {x}. What is it? The first, x, is an element . The second, {x}, is a set containing one element. For mathematical and other purposes, these two cases are distinct. Enumeration A set can be described as a list of the objects it contains (a list of its members). This is called enumeration . A list is put between braces: { } . A = {1, 12, 34, 65, 98, 119} C = {terrible, tortoise, tundra, tiddlywink} The order of objects in a list does not matter. Description We may use a description of the members of a set rather than an enumeration. T = {x | x is an English word starting with „t‟} “T is the set of all English words starting with the letter „t‟”. Elements The objects in a set are called elements or members . means ‘is an element of’ means ‘is not an element of’ A = {1, 12, 34, 65, 98, 119} 34 ∈ A 35 ∉ A Questions… Q: Can a set have any number of elements? A:
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set theory - Introduction Set theory is fundamental to...

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