This document provides an introduction to sets and the real number system. It defines key concepts such as elements, membership, cardinality, types of sets including finite, infinite, empty, subsets, proper subsets, improper subsets, universal sets, power sets, and set relations like equal, equivalent, joint, and disjoint sets. Examples are provided to illustrate each concept. The last section provides a quiz to test understanding of basic set concepts covered.

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

2. 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.

3. 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}

4. 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}

5. 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


6. 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

7. 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

8. 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}

9. 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.

10. 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.

11. 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


12. 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.

13. 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

14. 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

15. 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

16. 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}

17. 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.

18. 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.

19. 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.

20. 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.