2.1 - M316K(need to write in set builder notation Section...

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M316K (need to write in set builder notation) Section 2.1 - In mathematics, we use set language in may situations. Many mathematical concepts and operations are defined in set language, and set language is often useful when we are talking about mathematical situ- ations. - ex. set of even numbers - Sets as a Classification Tool - Children use ideas in everyday life as they look for similarities and differences between sets (ex. Why lions are in the cat family) - Defining Sets - Set: a collection of objects - Subset: classified smaller groups of a set; set that is part of some other set - Members or Elements: the individual objects in a given set - the symbol ∈ means “is a member of” - the symbol ∉ means “is not a member of” - Describing Sets - There are three different ways to describe sets: - We can use words - We can make a list - We can make a set-builder notation - Words and Lists - Natural numbers: the first set of numbers that young children learn - In words: N is the set of natural numbers or counting numbers - In list: N= {1,2,3,. ..} <--the braces indicate a set, three dots referred to as an el- lipsis and are used to indicate that the established pattern continues indefinitely. - Whole numbers: children will realize that zero is also a number - In words: W is the set of natural numbers and zero. - In list: W= {0,1,2,3,. ..} - Integer: children will become aware of negative numbers - In list: I= {. ..-3, -2, -1, 0, 1, 2, 3,. ..} - Set-builder Notation: - Rational Numbers: the set of all numbers that can be represented as the ratio of two in- tegers as long as the denominator is not zero. (This cannot be represented by making a list)
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This note was uploaded on 02/21/2009 for the course M 316K taught by Professor Ermer during the Spring '09 term at University of Texas.

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2.1 - M316K(need to write in set builder notation Section...

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