1. Negative
   Sub-prime
2. Delayed
   Irrational

Negative numbers are any real numbers that are less than zero, essentially making them the absence of a number. Our good friend zero doesn't qualify as either a positive number or a negative number.

1. Real
   Full
2. Prime
   Positive

As you likely learned in school, a prime number can only be divided by itself and the number one. So 2, 3, 5, 7, etc. The highest prime number calculated so far is over 23 million digits long and is called M77232917.

1. Fresh
   Transcendental
2. Prime
   Computable

It makes sense when you stop to think about it that any number a computer can handle is called computable. You could also use the terms recursive numbers or effective numbers to mean the same thing.

1. Surd
   Natural
2. Fuzzy
   Perfect

Natural numbers are just the numbers that you use to put things in order or count. So if you have 10 cats in a room, you'd count 1 to 10 to get to those cats and each one is a natural number. There's nothing fancy here.

1. Even
   Surreal
2. Integer
   Fraction

When you only have a piece of a whole, you have a fraction of the whole and that's what a fraction is. One half, one fifth, thirteen sixtieths and so on. It's a non-integer represented as a ratio of two integers. Fun!

1. Composite
   Prime
2. Ordinal
   Fraction

An ordinal number is a number that identifies a place in a list or sequence. So the number 2 is not ordinal but 2nd is ordinal because you now know it holds the number 2 spot in a sequence.

1. Superreal
   Unreal
2. Subreal
   Extra real

Much like hyperreal and surreal, superreal numbers take real numbers into an extended realm that is exceedingly complex and part of an abstract kind of algebra. It's safe to say most people will happily live their lives never knowing a superreal number.

1. Hypercomplex
   Surreal
2. Prime
   Imaginary

Hypercomplex numbers date back to mathematics in the 1800s, when mathematicians were looking for a way to explain and classify number systems ranging from real numbers to quaternions to octonions.

1. Cardinal
   Transfinite
2. Algebraic
   Negative

Cardinal numbers, in more technical terms, are numbers that measure the size of a set. In very basic layman's terms, cardinal numbers are numbers you use to count something. So when you describe how much of something is in a set you use a cardinal number. Got 5 baseballs? Five is a cardinal number.

1. Sexagesimal
   Hexadecimal
2. Composite
   Computational

The decimal system works on a base 10, the sexagesimal system works on a base 60 and was devised quite a long time ago by the Sumerians. This one dates all the way back to 2000 to 3000 BC.

1. Fractions
   Integers
2. Negative
   Odd

Odd numbers are not able to be evenly divided by two and are, for the most part, some of the first kinds of numbers a child will ever learn about in a math class. Oddly enough, the Greeks didn't consider 1 to be an odd number, but they didn't consider it even, either.

1. Quantum
   Infinitesimal
2. Hyporeal
   Below threshold

While something infinite has an endless bigness to it, something infinitesimal basically has infinite smallness. That sounds silly, but it's an easy way to describe something so small you have no real way of measuring it.

1. Integer
   Fuzzy
2. Nominal
   Surreal

In theory, this is hard to understand but in practice, nominal numbers make all the sense in the world. Lebron James has the number "23" on his jersey. That doesn't mean there are 23 jerseys or 23 Lebrons. It's just a nominal number that has no actual, numerical value.

1. Positive
   Whole
2. Fractals
   Even

Even numbers are most simply characterized by their ability to be divided into two. Any even number, divided by two, becomes half of itself and is still a whole integer with no fractions involved. Pretty simple stuff!

1. Fuzzy
   Algebraic
2. Incomplete
   Neutral

If a complex, and that includes real, number is the root of a non-zero polynomial it's an algebraic number. That's pretty much every single number in the world except transcendental numbers like pi.

1. Observed
   Superreal
2. Fuzzy
   Transcendental

Pi is a transcendental number and so is Euler's number. To be a transcendental number, a number has to not be algebraic but it does have to be real or complex. It's kind of hard to show that a number is transcendental

1. Complex
   Irrational
2. Obtuse
   Odd

When you get a real number, which is nearly any number, and an imaginary number, which is any number that gives you a negative when you square it, you can bring them together in a complex number.

1. Unreal
   Hyperreal
2. Subreal
   Parareal

Hyperreal numbers got their name in 1948 and are an extension of real numbers that extend to infinite numbers while their reciprocals extend in infinitesimals. It's a somewhat complicated system you can use in calculus.

1. Surreal
   Binomial
2. Imaginary
   Positive

If you square a number and get a negative, that's an imaginary number. Even though you can do math with these numbers, the term was coined by Rene Descartes to actually make fun of the very idea of them existing.

1. Tap
   Bit
2. Hex
   Pin

Hex is short for hexadecimal which is the base 16 number set used very often in computer coding. It generally uses the digits 0 through 9 and then the letters A through to F to represent all 16 digits. You might have noticed this term used in "The Martian" to talk about how Mark Watney communicated with Earth.

1. Complex
   Composite
2. Surreal
   Rational

In math language, you need to divide two integers to make a rational number. In simpler terms, if you can express the number as a fraction, which you can with most numbers, then it's rational. Even a single number like 10 can be expressed as a fraction (10/1) which means it's rational.

1. Positive
   Real
2. Prime
   Cardinal

A real number is mostly any number you can imagine, but not every number. If you can represent it as a distance on a number line, positive or negative, it's real. But infinity, or imaginary numbers, don't meet that criterion and can't be real.

1. Supernatural numbers
   Real numbers
2. Binary numbers
   Hypercomplex numbers

Ernst Steinitz is credited with creating supernatural numbers which is why they are sometimes called Steinitz numbers. They can be used to encode algebraic extension of a finite field and are also known as generalized natural numbers.

1. A whole number
   A fraction
2. An imaginary number
   A geometric number

Integers are just whole numbers, which is to say any number can be an integer like 10, 1000 or -100. That said, a number like 10.5 is not an integer because of the fraction. An integer is complete and whole on its own.

1. Surreal numbers
   Fuzzy numbers
2. Vague numbers
   Lost numbers

Surreal numbers are one of those hard concepts to grasp because they involve an ordered class of real numbers but then also some infinite and infinitesimal numbers to either side of that real number that are never greater or equal to the number of the other side. It's weird stuff. Surreal, even.

1. Hyperreal
   P-adic
2. Potential
   Supernatural

P-adic numbers are some of the hardest number to wrap your head around if you're not a math person. It's remarkably hard to explain what a p-adic number even is beyond saying they're used in number theory to allow for having that base "p" which can be any number and infinite integers to the left of the decimal instead of to the right. Google it if you like!

1. Transcendental
   Surreal
2. Composite
   Rooted

Composite numbers are fairly simple to understand even in terms of how they're named. Multiply two numbers together and the result is a composite because it is composed of those two numbers. That's math and English working together! Oh, and they have to be positive integers, too.

1. Rational
   Integer
2. Positive
   Binary

While negative numbers are under zero a positive number is any real number that is over zero. Negative and positive numbers are generally some of the easiest concepts for people to grasp when it comes to math.

1. Quick
   Strange
2. Zippy
   Fuzzy

A fuzzy number is not a specific integer. Rather it can be better understood as a range of numbers in a set between 1 and 1000. It's kind of like the mathematical version of guesstimating.

1. Gaussian integers
   Fibonacci numbers
2. Quadratic surds
   Algebraic numbers

Having both real and imaginary parts that are integers is what defines a Gaussian integer. If you've never run across the word "Gaussian" before, you're missing out on a very fancy way to say "normal curve or normal distribution."

1. Constructible
   Geometrical
2. Infinitesimal
   Binomial

A constructible line is true to its name and it is something you can construct. Using only a compass and a ruler and a finite number of steps, if you can construct a line you can call that line constructible.

1. Rudimentary
   Simplified
2. Binary
   Computable

The basics of computer programming are often done in binary where coding is represented simply as a series of 0s and 1s. A number is binary if it's in that kind of relationship where it's a base-2 system.

1. Irrational
   Full
2. Prime
   Positive

If a number can't be shown as a simple fraction, it's an irrational number. A famous example of that would be pi which is impossible to represent as a fraction. Likewise, a number like the square root of 2 can't be represented that way and that means it's irrational also.

1. Fraction
   Irrational
2. Surd
   Composite

If you can't get to the square root of the number, it's a surd. So when you write out root 16, that can be simplified down to 4, so it's not a surd. But if you want to do root 2 you can't simplify it, so it is a surd.

1. Composite
   Press sum
2. Erluen's number
   Fibonacci number

Fibonacci numbers work in what is usually called a Fibonacci sequence or series in which a number is the sum of the two preceding numbers. They're named for Leonardo of Pisa who later, of course, came to be known as Fibonacci.