Sets of Real Numbers

• A set is a collection of objects.
• An object in a set is called an element of that set.
• Different type of integers:

1. Set of Positive Integers = {1,2,3, ...}
2. Set of Negative Integers = (..., -3,-2,-1}

• The real-number line is shown as:

Some Properties of Real Numbers

• Important properties of real numbers

1. The Transitive Property of Equality

If a=b and b=c then a=c

2. The Closure Properties of Addition and Multiplication
3. The Commutative Properties of Addn and Multiplicationition
4. The Commutative Properties of Addition and Multiplication

5. The Identity Properties

6. The Inverse Properties

7. The Distributive Properties

Review of Algebra

The Objective of Review Algebra

• To be familiar with sets, real numbers, real-number line.
• To relate properties of real numbers in terms of their operations.
• To review the procedure of rationalizing the denominator.
• To perform operations of algebraic expressions.
• To state basic rules for factoring.
• To rationalize the denominator of a fraction.
• To solve linear equations.
• To solve quadratic equations.

Content of Review Algebra:

1. Sets of Real Numbers
2. Some Properties of Real Numbers
3. Exponents and Radicals
4. Operations with Algebraic Expressions
5. Factoring
6. Fractions
7. Equations, in Particular Linear Equations
8. Quadratic Equations

MATHEMATICAL for BUSINESS

Review of Algebra
Applications and More Algebra
Functions and Graphs
Lines, Parabolas, and Systems
Exponential and Logarithmic Functions
Mathematics of Finance
Matrix Algebra
Linear Programming
Introduction to Probability and Statistics
Additional Topics in Probability
Limits and Continuity
Differentiation
Additional Differentiation Topics
Curve Sketching
Integration
Methods and Applications of Integration
Continuous Random Variables
Multivariable Calculus