Basic Operations Number Types

Natural Numbers (a.k.a. Counting Numbers)

Thinking of natural numbers, we can transport ourselves back to simpler times. The good ol' days when our only responsibility was to show up for kindergarten class and not wet our pants. Aahhh, memories. It was at this point that we solidified our counting skills, and counting is what natural numbers are all about.

Natural numbers, also known as counting numbers, start with 1 and go on forever. The numbers 1, 2, 3, 4, 5,… are all natural numbers.

We use natural numbers, like 1, 2, 3 and so on, to count objects, days, people, hairless cats, hairy hippos, whatever. When we use natural numbers to count, we can refer to them as cardinal numbers. We also use natural numbers to order things, like ordering classmates from shortest to tallest. In these cases, we refer to them as ordinal numbers and write them as 1^st, 2^nd, 3^rd, etc.

For more info on natural numbers, go here.

Whole Numbers

Whole numbers are very similar to counting numbers. Their only difference is the fact that whole numbers include the number zero. When we list whole numbers from least to greatest, we get 0, 1, 2, 3, and so on and on and on.

Whole numbers are a quirky bunch with some pretty strong character traits. We love them for their optimistic, the-glass-is-half-full approach to mathematics. They never accept negative numbers (or pouting) into their group, and they don't take any trash talk. Whole numbers also pride themselves on their goody-two-shoes wholeness, which means fractions and decimals aren't welcome either. They're pretty exclusive like that.

For more honest-to-goodness whole number examples, check this out.

In the image above, the whole numbers are made up of every number in the big box, including the contents of ur you-know-whats off at -10 degrees. Temperature measured in Fahrenheit and Celsius can be positive or negative, and this is what makes integers different from whole numbers.

Integers include all of the whole numbers, their opposites, and zero. No, not opposite as in "evil twin," but opposite as in negative. For example, the opposite of 5 is (the oh-so-moody) -5. The opposite of 10 is (the even moodier) -10.

That makes the integers, {…, -3, -2, -1, 0, 1, 2, 3, …}.

Although integers are tolerant and inclusive of negative numbers, they're pretty strict about wholeness, which means fractions and decimals aren't welcome. Hey, they've gotta draw the line somewhere.

For more on integers, visit here. Just be prepared to take the good with the bad.

There are now three boxes. Numbers that are allowed in the biggest box, a.k.a. the integers, include all the numbers in the smaller boxes as well. So integers include negative numbers, whole numbers, and natural numbers.