- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
**In the Real World**- Decimals in Use
- How to Solve a Math Problem
**I Like Abstract Things: Summary**

Okay, so you're a dreamer. There's plenty in algebra for you, too. Just think: we've touched on the concept of infinity, which is pretty far out there. Even if you were immortal (you're not), you couldn't finish reading the decimal representation of a single irrational number. Plus, there are so many irrational numbers that you can't possibly list them all. However, we can list all the *rational* numbers, which means that, although there are infinitely many rational numbers, there are still more irrational numbers than rational numbers.

Mind. Blown.

These ideas are part of set theory, which addresses what it means to "count" collections of infinitely many objects. (You know, like Jay Leno's car collection.)

We've also started proving theorems, such as the fact that the square root of 2 is irrational. Most of mathematics is more about proofs than about arithmetic, but arithmetic is a good place to find some interesting proofs. So is a photography studio, come to think of it.

Let's continue on to Algebraic Expressions!