Presentation top top theme: " A collection is a repertoire of objects. Each object in the collection is dubbed an facet or member of the set. Example. Permit A be a collection of 3 markers."— Presentation transcript:




You are watching: A collection of objects is called

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2  A set is a arsenal of objects. Every object in the set is dubbed an facet or member that the set. Example. Allow A it is in a collection of three markers. Example. Let B it is in the set of students at this time enrolled in this ar of MAT 142. Note: The bespeak of listing elements in the collection has no effect on the set itself. The set of the 3 students Bob, Ellen and Kaye is the very same as the collection Ellen, Bob and also Kaye.

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3  The collection of counting numbers 1, 2, 3, 4, 5, … is dubbed the set of organic Numbers. The collection of herbal numbers is denoted N. ◦ Note: The three durations in this definition are called ellipses and also mean that you should proceed with the established pattern.  The collection containing no facets is referred to as the north set, or null set. The null set is denoted by , or by the tiny Greek letter phi,  ◦ Note: The curly braces in this definition are called collection braces.

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4  I. Native Description: let A be the collection of organic numbers much less than 3.  II. Set-Builder Form: ◦ A = {x | x is a herbal number, x

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5  Write set B in roster form. ◦ B = k  Answer: B = 2  Write set C in roster form. ◦ C = m is a organic number, m 1  OR x

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6  A collection is well-defined if any kind of informed objective person can decide if a given facet is in the collection or not.

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7  A is the collection of goofy dogs.  B is the collection of GCC students whose gpa is 3.0 or greater.  C is the collection of great GCC students.  D is the set of numbers who square is 16. Answer: B and also D. Note that D = -4, 4.

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8  5  A means “5 is an element of the set A.”  when you watch the notation 5  A, it way that 5 will certainly be in the perform if you write A in roster form. 2 sets are equal if they contain precisely the very same elements.

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9  1, 2 = 2,1   =   = 0   =   0,1 = 1  1  1, 2  0  1, 2  1  1, 2  0  1, 2  True. (Same elements)  False. ( 0 is not empty.)  False. (  is no empty.)  False  True  False  True

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10  A universal collection for a particular problem is a set which includes all the elements of all the to adjust in the problem.  A universal set is regularly denoted by a resources U.

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11  A = 1, 2, 3  B = 2, 4, 6, …  C = 28 One answer: permit U it is in the collection of natural numbers.

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12 A: The set of people who are right now enrolled in a math course at GCC. B: The collection of people enrolled in a physical education course at GCC. C: The set of human being enrolled in the nursing regimen at GCC. One answer: let U be the set of people at this time enrolled in classes in ~ GCC.

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13  A collection is limited if the is possible, given sufficient time, to compose down every element in the set.  A collection is boundless if it is no finite. Example. The collection 1, 2, 3, …, 1000000000000000 is finite. It i will not ~ be funny to actually create every element in this set, yet it is possible given sufficient time. Example. The collection 1, 2, 3, … is infinite.

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14  The cardinal variety of a collection A is denoted n(A).  find the cardinal number of the following set A. ◦ A = {x | x  N, 2

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15  Finite set A is indistinguishable to set B if n(A) = n(B).  If two sets are indistinguishable it method that they have the right to be put into one-to-one correspondence. Take it A=1,2,3 and B=a, b, c. One such correspondence deserve to be viewed graphically: 123123 abcabc

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16 n(1,2) = n(x,y) True. The cardinal number of both to adjust is 2. N(  = n(0) False. N(  )=0 but n(0)=1. In other words, the empty collection contains no aspects but the collection on the right has one element, specific the number 0. 1,2 = x,y False. The 2 sets execute not save the exact same elements. 1,2 is tantamount to x,y. True. Both sets contain the same variety of elements.

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17 1. Perform the complying with sets in roster form. A.A= x is a organic number, 2x=12 b.B= x is a herbal number, -3k=12 2. Is the collection of scary cat a well-defined set? Why or why not? 3. True or False. N(x is a herbal number much less than or same to 5)=n(w, x, y, z). Provide a reason for her answer. 4. Give an instance of 2 sets which are equivalent however not equal.

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5. Why no  same to the number 0?

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