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Yes, you can access Introduction to Calculus by Joan Van Glabek in PDF and/or ePUB format, as well as other popular books in Study Aids & History of Art. We have over one million books available in our catalogue for you to explore.
This chapter contains a short review of some of the algebraic topics that will be encountered in the remainder of the book. We review the real number system, interval notation, solving inequalities, and graphing in the Cartesian plane.
REAL NUMBERS, INEQUALITIES AND ABSOLUTE VALUE
REAL NUMBERS
The study of calculus involves real numbers. The union of the set of rational numbers (numbers that can be written as a ratio of two integers) and the set of irrational numbers (numbers that cannot be written as a terminating or repeating decimal) is the set of real numbers.
Irrationals
Rationals
ORDER
Compare real numbers using the following symbols:
< less than
≤ less than or equal to
> greater than
≥ greater than or equal to
For example,
means
lies to the left of
on the number line.
INTERVAL NOTATION AND SET NOTATION
In this book, we use subsets of the real numbers as solutions to equations or inequalities. These subsets are usually described using either interval notation or set notation as demonstrated in the following table.
Interval Notation
Set Notation
Graph
(–1, 3)
{x: - 1 < x < 3}
[–1. 3]
{x: - 1 ≤ x ≤ 3}
(–1, 3]
{x: - 1 < x ≤ 3}
[–1, 3)
{x: - 1 ≤ x < 3}
Notice that a parenthesis corresponds to an endpoint...
