Sets Part I The Basics

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Information about Sets Part I The Basics

Published on May 8, 2009

Author: siegeable

Source: slideshare.net

Description

A student's f*cked up guide to Set Theory in Mathematics for an easier and non-pointless Algebra.

SETS AND THE REAL NUMBER SYSTEM A Crash Course for Algebra Dummies

Lesson One: The Basics Why the concept of sets is actually hated by most humans – and why it has become one of the most reasonable widely-accepted theories.

What is a set? A SET is a well-defined collection of objects.  Sets are named using capital letters.  The members or objects are called  ELEMENTS. Elements of a set may be condoms, dildos, dick wads, as long as they herald a common TRUTH. Denoting a set would mean enclosing the  elements in BRACES { }. S = {3, 6, 9, 12, 15}

Ways To Define Sets Rule Method – defining a set by describing the 1. elements. Also called the descriptive method.  A = {first names of porn stars Chad knows}  B = {counting numbers} Roster Method – defining a set by 2. enumerating the members of the set in braces. Common elements are only written once. Each element is seperated by a comma. Also called the listing method.  A = {Brent, Dani, Jean, Jeff, Luke, Chloe}

Ways to Define Sets Set-builder Notation – commonly used in 3. areas of quantitative math to be short. Like the rule method. This definition assigns a variable to an element such that all values of the variable share the truths of the elements of the set. A = {m|m is a porn star Chad knows}  Set of all m such that m is a porn star Chad  knows B = {x|x is a counting number}  Set of all x such that x is a counting number 

Set Membership This is the relation telling us that a thing is  an element of a particular set. ∈ is the symbol for “is an element of”. This  is a symbol used in set-builder notation. P = {yellow, red, blue} yellow ∈ P green ∉ P

Cardinality The CARDINALITY of a set states the number  of elements a set contains. The cardinality is expressed as n(A), wherein A is the given set. G = {a, s, s, h, o, l, e} n(G)= 7 R = {fucking, sucking, rimming, ramming} n(R)=4 A = {how many balls a person has} n(A) = 2

Exercise One: Defining Sets Set H is the set of letters in the word 1. PORNOGRAPHY. Write it using the roster method.  H = {P, O, R, N, G, A, H, Y} X = {I, V, X, C, L, D, M}. Describe the set and 2. state its cardinality.  X = {letters used to denote Roman numerals}. n(X)= 7. Set Z is the set of all condom brands. Write it 3. using the set-builder notation method.  Z = {x|x ∈ condom brands}

Kinds of Sets Empty Sets or Null Sets – sets with no  elements.  A = {girls in New York St. that have dicks}  A = { } or A = Ø. The set has 0 cardinality. Infinite Sets – sets with an infinite number of  elements. Unlisted elements are denoted by ellipses.  F = {x|x is a number} Finite Sets – sets with an exact number of  elements.  H = {penises Chad has}. n(H)= 27.

Exercise Two: Kinds of Sets Write the set of whole numbers less than 0. 1. Define what kind of set it is.  A = Ø. It’s a null set. Explain which of the following is finite: the set 2. of the vowels in the English alphabet or the set of cum shots all the boys in the world make.  The first set is finite. There are only five vowels, as compared to the expanding number of cum shots, which makes the second set infinite.

Set Relations Equal Sets – sets having the exact same  elements.  If A = {F, U, C, K}, B = {letters in “FUCK”}, and C = {F, C, U, K}, then A = B = C. Equivalent Sets – sets with equal number of  elements. All equal sets are equivalent. But not all equivalent sets are equal.  F = {x|x is a letter of “CUM”} & G = {W, A, D}  Both sets have 3 elements, making them equivalent. Groups of equivalent sets and groups of 

Set Relations Joint Sets – sets having common elements.   If A = {body parts of girls},  B = {body parts of Rosie O’Donell}, then  A and B are joint sets since both contain vagina. Disjoint Sets – sets having no common  elements.  F = {penis} & G = {body parts of girls}  They are disjoint because penis is not a body part of girls.

Universal Sets and Subsets The UNIVERSAL SET (U) is the set containing  all elements in a given discussion. It contains every other set that is related to the discussion. SUBSETS are sets whose elements are  members of another set. It is formed using the elements of a given set. The symbol ⊂ denotes “is a subset of”. G = {d, i, c, k, h, e, a} Y = {d, i, c, k} Y⊂ G

Subsets Every set is a subset of the universal set. (S ⊂  U) There are two types of subsets.  Proper Subset – a set whose elements are 1. members of another set, but is not equal to that set.  Given W as the set of whole numbers and E as the set of even numbers, then E ⊂ W. 2. Improper Subset – a set whose elements are members of another set, but is equal to the set.  Given M as the set of multiples of 2 and E as

Subsets Every set is an improper subset of itself. (S ⊆  S) The null set is a proper subset of any set. (Ø ⊆  S) For any two sets A and B, if A ⊂ B and B ⊂ A,  then it means A = B. The number of subsets for a finite set A is given  by: n(A) 2

Subsets The subsets of the set The number of M = {x, y, z} are: subsets is given by: • Subsets = 2n(M) • Ø • • Since n(M) = 3, then {x} n(M) 3 • 2 =2 {y} • 23 is equal to 8. • {z} • You will see that the • {x, y} number of subsets on • {y, z} the left is 8 too. • {z, x} • {x, y, z}

Exercise Three: Subsets Write all the SUBSETS of the set N = {s, h, i,  t} in one set. Name this set NS. This is called the POWER SET of the set N. State the cardinality of set NS. One: NS = {Ø, {s}, {h}, {i}, {t}, {s, h},  Answer {s, i}, {s, t}, {h, i}, {h, t}, {i, y}, {s, h, i}, {s, h, t}, {h, i, t}, {s, i, t}, {s, h, i, t}}  The cardinality of this set is given by the n(N) formula 2 . Since N had four elements, the expression became 24, which led to n(NS) = 16.

Quiz One: Basic Concepts For every slide you are given five minutes to answer. Points depend on the difficulty of the question. Do not cheat or I’ll kick your ass.

Two-Point Items Write what is asked. • The set of numbers greater than 0. Use Set Builder Notation. State the type of set. • The set of months of the year ending in “ber”. Use listing. State cardinality of set. • The set of all positive integers less than ten. Create another set to disjoin with this set. • The set of the letters in SEX. Provide an equivalent set.

Three-Point Items Write the power set of set P = {i, l, y}. State the cardinality of the power set. Given that W is the set of days in a week. How many subsets does this set have? Is there any improper subset in those sets? If so, write down that improper subset of W.

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