Chapter 0: Algebra Review Flashcards
We use the term interval for
When a < b, we use (a, b) to indicate the set of all real numbers between an and b, including neither a nor b.
So (a, b) is the interval from a to b.
If we wish to include an endpoint in an interval, we use a … to show it
square bracket, as in [a, b)
We write the set consisting of a single number a as __
{a}
If we want to indicate the set of all numbers less than , we use
(-∞,a)
Sometimes it is convenient to describe intervals and other sets using set-builder notation. For example, the interval (a, b) can be written as
{x: a < a < b}. We read this as “The set of all 𝓧 such that a < x < b.
concepts to remember in interval notation
what is the the complement of the interval?
Sometimes we want to refer to the set of all numbers not belonging to a certain interval
The complement of an interval consists of all real numbers that are not in the interval.
what is a union of the intervals
Sometimes the complement of an interval consists of two intervals. We call such a set the union of the intervals.
The union of two sets consists of all elements belonging to one or both of the sets.
an intiger
include the counting numbers, their negatives, and zero
The rational numbers are
Irrational numbers are
Real numbers are denoted by the symbol
The real numbers consist of
of the rational numbers together with the irrational numbers.
The real number line is
1
Absolute Value
triangle inequality
LAWS OF MATHEMATICS:
Absolute Value
Absolute Value as Distance
LAWS OF MATHEMATICS:
Distance and Absolute Value
The distance between x and y on the real line is
nth root
more on nth roots
LAWS OF MATHEMATICS:
Roots and Powers
laws of mathematics for completing the square
the quadratic formula
