Study Guide

# Types of Numbers - Even and Odd Numbers

## Even and Odd Numbers

The words "even" and "odd" have several meanings in mathematics. If we're talking about numbers, an even number is an integer that's divisible by 2 with nothing left over. Yes, it's a major bummer when there are no leftovers, but even numbers aren't really that delicious in the first place, so it's not a huge loss.

Here are some even numbers:

...-6, -4, -2, 0, 2, 4, 6...

Yep, 0 is even, because 0 can be divided by anything with nothing left over. That means 0 ÷ 2 = 0, so it's even.

If we were to continue filling in that list in both directions forever, we would get all the even numbers. Although, since there's an infinite amount of them, we'd need an awfully long scroll bar over there →

An odd number is any integer that's not divisible by 2. Try to divide these guys by 2 and we'll always have 1 or -1 left over. (Great; that'll be tomorrow's lunch.) In other words, any integer that's not even is odd. Here are some examples:

...-7, -5, -3, -1, 1, 3, 5, 7...

Every integer must be either even or odd, 'cause every integer is either divisible by 2 or not divisible by 2. There are no other possibilities. And that's not just us being pessimistic. It's a fact, yo.

• ### Infinity

Something is finite if it comes to an end. (Like this Algebra study guide, believe it or not.) A book or movie is finite: after you've turned the last page or watched the final credit, it's over. A day is finite: after 24 hours, the clock calls it a wrap and starts over with a new one. Your body takes up a finite amount of space: you have skin (hopefully on the outside), and there your body ends.

Something is infinite if it does not have an end. Infinity is not a number but a concept. The counting numbers, for example, are infinite: if you start counting and try to count as high as you can, you'll never finish because you'll never run out of numbers. Unless you can only count to 100, in which case, jolly good show.

Fractals are also infinite: no matter how much you zoom in, you can always zoom in more.

For those who like silly books, The Phantom Tollbooth has a wonderful description of infinity in Chapter 15, "This Way to Infinity." You can also try David Foster Wallace's Infinite Jest, which is so lengthy it's also almost an "infinite read."