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FINAL Semester #1
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Terms in this set (57)
A set
collection of objects, named using capital letters
Elements/Members
Objects of the set, no object is listed more than once
3 ways to specify sets
Description, Roster, Set Builder Notation
Description
within {} write sentence identifying elements in the set
Roster
List of the elements within {}
Set Builder Notation
{variable/variable E set and condition to be satisfied} NOTE: / means such that, E means element of
Sets of #s
N, W, Z, Q, I, R
N
Natural #s 1,2,3...
W
Whole #s 0,1,2,3...
Z
Integers #s ...-3,-2,-1,0,1,2,3...
Q
Rational #s, all #s that can be written as ratio of 2 integers, all #s with repeating or terminating decimals
I
Irrational #s, all #s that we cannot express as a ratio of 2 integers, all #s that are not rational, all #s with non-repeating/ terminating decimal
R
Real #s, any # that is rational or irrational
The union of 2 sets
is the set containing all of elements of set A together with all elements of set B denoted as AUB
Intersection of 2 sets
Set containing those elements in both sets AupsidedownUB
Subset
A is the subset of B iff every element of set A is also an element of B. Denoted as AsidewaysUB. Every set is a subset of itself. Empty set is a subset of every set.
Equal Sets
two sets A and B equal iff they are subsets of each other. Denoted as A=B
Disjoint sets
two sets are disjoint if A intersection B = empty set
Reflexive Property of Equality
a=a, any # is equal to itself
Symmetric Property Equality
a=b than b=a allows us to swap sides of the equation
Transitive Property Equality
if a=b and b=c then a=c
Addition Property Equality
a=b then a+c=b+c works for subtraction
Multiplication Property Equality
a=b then axc=bxc works for addition
Substition Property of Equality
equals can be substituted for each other
Communicative Property of Addition
a+b=b+a the order in which we add is NOT important
Communicative Property of Multiplication
ab=ba the order in which we multiply is NOT important
Associative Property of Addition
(a+b)+c=a+(b+c) we can change the grouping while leaving the order the same
Associative Property of Multiplication
(ab)c=a(bc) we can change the grouping while leaving the order the same
Distributive Property of Multiplication over Addition
a(b+c) = ab+ac
Closure Property of Addition
the sum of 2 real #s is a real #
Closure Property of Multiplication
the product of 2 real #s is a real #
Additive Identity
0 because for all real #s a+0=a
Additive Inverses
a+b=0 every real # has one
Multiplicative Identity
1 because for all real #s ax1=a
Multiplicative Inverses
when ab=1, every real # except 0 has one
Conjunction
a mathematical or statement containing the word AND. To be true, both of the clauses must be true
Disjunction
a mathematical or statement containing the word OR. To be true, either or both clause must be true
Absolute Values can not...
be negative!
x^0 =
1
(A-B)^3
(A-B)(A^2+AB+B^2)
(A+B)^3
(A+B)(A^2-AB+B^2)
When we have option of factoring as difference of squares or a difference of cubes go for...
Difference of squares 1st
Rational Expression
an algebraic fraction = ratio of 2 polynomials
Complex Fraction
a rational expression with a rational expression in it's numerator, denominator or both
i
pure imaginary #
with i^n - if n is odd and one more than multiple of 4
i
with i^n - if n is odd and one less than multiple of 4
-i
with i^n - if n is even and a multiple of 4
1
with i^n - if n is even and not a multiple of 4
-1
3^4
81
6^3
216
6^4
1296
7^3
343
3^5
243
4^5
1024
5^5
3125
Absolute Values
|x|=5 means x=5 or x=-5
|x|>5 means x>5 or x<-5
|x|<5 means -5<x<5
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