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Information about Sets Part I The Basics

Published on May 8, 2009

Author: siegeable

Source: slideshare.net

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

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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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