## 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:

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