SetTheory

# SetTheory - SET DEFINITIONS 1 5 9 13 Item set 2 6...

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1 SET DEFINITIONS Item Definition Designation example set collection of objects {1,3, 5,7} my deck of cards is a set of cards Empty set a set has nothing in it \ Subset A is a subset of B, designated by A B or B A if all members of A are members of B U = {x Z : P(x)} where P(x) means 1 x 7, x is odd this uses subsets to define the sets Equal sets Two sets are equal if they contain the same elements, i.e., A B and B A Proper subset A B and B A Number designations R or R collection of real numbers < or Q collection of rational numbers, that is consists of p/q where p and q are integers Z or Z collection of integers: …, -2, -1, 0, 1, 2, ... N or N collection of positive integer (does not include 0) : 1, 2, … Intervals Let a,b R (a,b) = {x R : a < x < b} bounded open interval [a,b] = {x R : a x b} bounded closed interval [a,b) = {x R : a x < b} bounded half-open interval (a,b] = {x R : a < x b} bounded half-open interval (a, ) = {x R : x > a} unbounded open interval (- ∞,b ) = {x R : x < b}

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