#### CHECK OUT SHMOOP'S FREE STUDY TOOLS: Essay Lab | Math Shack | Videos

# Algebra Introduction

# Recognizing Different Types of Numbers

Ever run into someone who is *super* excited to see you, but you just can’t place him to save your life? You make some polite small talk about the weather and try desperately to act like you're not experiencing the world's biggest brain fart, but somehow you always get to that moment when he realizes that you have no idea what is going on...or who he is. Cue awkward silence.

Yeah, that’s not a great feeling.

Here's the good news: when it comes to numbers, you're starting with a clean slate. Learn to recognize each type of number at a glance, and you’ll never be caught in any uncomfortable situations. Trust us—you don’t want to fail to recognize an irrational number. They can fly off the handle at the slightest provocation.

**Natural and Whole Numbers.**Natural numbers are the counting numbers, or the numbers that we use to count. Remember the Count from Sesame Street?*One*natural number, ah-ah-ah.*Two*natural numbers, ah-ah-ah. That guy sure knew his counting numbers.

Whole numbers are the same as natural numbers, but with the addition of zero. It just got sad watching zero hanging his head while sitting on the bench all day long, so whole numbers invited him to get into the game. Good for zero. You get ‘em, tiger.

**Integers.**The set of integers consist of all whole numbers, plus all their negative reflections. Zero is an integer, although he’s the only one without a reflection. (Probably a vampire.)

**Rational Numbers.**This is any number that can be written as the quotient of two integers, otherwise known as a fraction. This includes every integer, because every integer can be written as*x*/1. -34,823/4? Looks weird, but it's totally rational.

**Irrational Numbers.**As the name suggests, these buggers can be unpleasant to deal with. They cannot be expressed as a fraction, but instead are generally represented by a symbol so we have something to call them. π and are a couple of famous irrational numbers. We’ll try to get you their autographs, but please understand that they’re very busy.

**Real Numbers.**Gather up all your rational and irrational numbers, and you’ve got your set of real numbers. Basically, it’s every number that isn’t in the set of...

**Imaginary Numbers.**Yes, algebra allows you to use your imagination. In fact, your 8-foot-tall imaginary clown friend is even allowed to join you in the SAT testing room when you eventually get around to taking the test. He isn’t allowed to whisper any of the answers to you, however. That would be cheating.