This PDF document is designed to help you ace your college algebra tests. It's full of all the details, and it's written in a neat and concise way. You can print it out, or just read it on your computer screen.
If you're struggling with college algebra or if you need a little extra help, this PD...
0.1 Introduction
0.1.1 Definition
A set is an array of precisely defined and distinct elements, elements could be
any mathematical object: numbers, symbols, points in space, variables or even other
sets.
There are 3 types of sets:
1-Finite Sets: Arrays with a definite number of elements
S = {a, b, c, d}
2- Infinite Sets: Arrays with an indefinite number of elements
P = {2, 3, 5, 7, 11, ...}
3- Empty Set(Null Sets): A single array in which no elements are contained within
the set (Zero Entites), Denoted as:
E =∅
or
E ={}
0.1.2 Number Sets
N = {1, 2, 3, 4, ...} ⇒ Natural Numbers
Z = {0,
±1, ±2, ±3, ...} ⇒Integer Numbers
p
Q= |(p, q) ∈ Z, q ̸= 0 ⇒ Rational Numbers
q
R = {±x1 x2 x3 ...xn .y1 y2 y3 ...ym | 0 ≤ xi , yj ≤ 9} ⇒ Real Numbers
C = {z = a + bi | (Re(z) = a, Im(z) = b) ∈ R, i2 = −1} ⇒ Complex Numbers
3
, 0.2 Working With Sets
0.2.1 Subsets
Let A be a subset of W, this means that every element of A is in W and we write:
A⊆W
Example
. C = {1, 6, 8} D = {1, 2, 3, 6, 8, 9}
C is a subset of D or:
C⊂D
Thus every element of C is in D, but C ̸= D
0.2.2 Improper Subset
Every set is a subset of itself: this is the Improper Subset
A⊆A
Note
The empty set is a subset of every set
∅⊆X
Disjoint Sets
Two sets are said to be disjoint sets if they have no element in common. Equiva-
lently, two disjoint sets are sets whose intersection is the empty set ∅.
A B
A∩B =∅
4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller aamaralberm. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $25.48. You're not tied to anything after your purchase.
