Summary
Summary Mathematics 114
- Course
- Institution
- Book
A concise summary of Mathematics 114 at University Level. Full coverage of work from calculus to sets.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
danilgrtter
Content preview
Mathematics 114Number systems
R : real : 12, 3/4, pi, 1.3333
N : natural : (1, inf inity)
Q : rational, a/b, a ∈ K, b ∈ K, b ≠ 0
K : integer, (−inf inity, inf inity)0
Absolute values
negative turns positive
| − a| = a
Absolute Value Inequalities
1.Find values of x for which all values are positive
2.Find values of x between where one part is positive and other part negative
3.Find values of x where both parts are negative
4.Do the union of sets
|x + 2| > |x − 6|
case 1: x >= 6
x + 2 > x − 6
2 > −6
true for all values bigger than or equal to 6
case 2: 6 -2 <=x < 6
x + 2 > −(x − 6)
2x > 4
x > 4
case 3: x < -2
−(x + 2) > −(x − 6)
−2 > 6
false for all values smaller than -2
x>4
Sets
, #definition A set is a unordered collection of unique items
The set containing {1,2,3} is the same as {1,2,3,2,1,3,2,1}
(a,b) : all values between a and b : not inclusive
[a,b] : all values between a and b : inclusive
#definition a set is a subset of another set when it contains all the elements of the other set
eg: {1} ⅽ {1,2,3}
Set Builder Notation
A set can be expressed as the set of the variable where certain conditions are met
A = { a | predicate }
eg: A = {a | a ∈ R}
A is the set of all Real numbers
eg: B = {b | b ∈ N | b > 5 }
B is the set of all natural numbers higher than 5
Intersection and Union
The elements in one set and another
A∩B
The elements in one set or another
A∪B
Compliment
The set of all items not in a set
A / B = { x ∈ A | x ∉ B}
eg: {1,2,3} / {2,3} = {1}
Multiplication of Sets
The product of two sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where
a is in A and b is in B
eg: if A = {1, 2} and B = {a, b}, then A × B = {(1, a), (1, b), (2, a), (2, b)}.
Logic
A => B
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 danilgrtter. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.84. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81849 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now