# What Kind of Number Am I?

By: Ian Fortey Image: iMrSquid

Here's a weird question — do math and numbers exist apart from humans or because of humans? Did 2 plus 2 equal 4 before anyone existed who knew how to count to either 2 or 4? Some people would answer no to that question while others would say, of course, math has to exist independent of mankind. Two oranges on a tree will always be two oranges on a tree even if no one is ever around to see them.

The more you get into numbers the more clear it becomes that the math of the universe is something you can discover as sure as people discovered new lands when they went exploring back in the day. From the basics of simple counting to Pythagoras discovering his famous theorem in geometry to the complex arithmetic involved in calculus and quantum mechanics, there are far more numbers than your simple 1 to 10 counting. We went from straight numbering systems to understanding a difference between positives and negatives, rational and irrational, complex and hypercomplex and beyond. You can start to lose count of the kinds of numbers there are eventually. So before you lose track of where we are, why not take this quiz and see if these are numbers you can identify! What do you call any real number less than zero?
Negative
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.
Sub-prime
Delayed
Irrational This number has only 2 positive divisors, itself and 1. What is it called?
Real
Full
Prime
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.
Positive What can you call a real number that a finite computer algorithm can calculate?
Fresh
Transcendental
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. This is what you call numbers as you'd use them to count. Do you know what they're called?
Surd
Natural
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.
Fuzzy
Perfect What do you call a number that is a part of a whole?
Even
Surreal
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! Which numbers tell you where something is in a sequence?
Composite
Prime
Ordinal
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.
Fraction What numbers are an extension of real numbers?
Superreal
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.
Unreal
Subreal
Extra real What kind of number explains geometric operations beyond 2-dimensional planes?
Hypercomplex
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.
Surreal
Prime
Imaginary If you're counting out coins or buttons or peanuts, what kind of numbers are you using?
Cardinal
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.
Transfinite
Algebraic
Negative These numbers have a base 60 system. What are they?
Sexagesimal
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.
Composite
Computational Which of these numbers are defined as not being divisible by 2?
Fractions
Integers
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. What do you call a number too small to measure?
Quantum
Infinitesimal
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.
Hyporeal
Below threshold This term covers any number that describes or identifies something but doesn't hold that number's value. What is it?
Integer
Fuzzy
Nominal
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.
Surreal What kind of numbers are defined based only on the fact they're evenly divisible by 2?
Positive
Whole
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! Any complex number that is the root of a non-zero polynomial is called what?
Fuzzy
Algebraic
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.
Incomplete
Neutral Which of these describes pi?
Observed
Superreal
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 What do you get when a real and imaginary number come together?
Complex
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.
Irrational
Obtuse
Odd What numbers are an extension of real numbers?
Unreal
Hyperreal
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.
Subreal
Parareal What do you call a number that gives you a negative when you square it?
Surreal
Binomial
Imaginary
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.
Positive Computers often use these numbers that have a base 16. What are they called?
Tap
Bit
Hex
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.
Pin What do you call the kind of number you can get by dividing two integers?
Complex
Composite
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. This label applies to almost every conceivable number but not something like infinity. What is it?
Positive
Real
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.
Prime
Cardinal What do some people call Steinitz numbers?
Supernatural 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.
Real numbers
Binary numbers
Hypercomplex numbers What is an integer?
A whole 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.
A fraction
An imaginary number
A geometric number What kind of number was invented by John Conway and Donald Knuth in 1974?
Surreal 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.
Fuzzy numbers
Vague numbers
Lost numbers Kurt Hensel first described these very complicated numbers in 1897. What are they?
Hyperreal
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!
Potential
Supernatural Any number made by multiplying two smaller integers qualifies as what?
Transcendental
Surreal
Composite
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.
Rooted If something is a real number above zero, what is it?
Rational
Integer
Positive
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.
Binary Most numbers have precise values. Not these ones. What are they?
Quick
Strange
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. Which number is comprised of real and imaginary parts that are both integers?
Gaussian integers
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."
Fibonacci numbers
Algebraic numbers What do you call a number if you can make a line segment representing it with a compass and ruler?
Constructible
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.
Geometrical
Infinitesimal
Binomial This system is represented by 0s and 1s. What is it?
Rudimentary
Simplified
Binary
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.
Computable Which kind of number cannot be written as a simple fraction?
Irrational
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.
Full
Prime
Positive If a number can't be made simpler to remove a square root, what is it?
Fraction
Irrational
Surd
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.
Composite When each number in a series is the sum of the two numbers before it, what would you call it?
Composite
Press sum
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. 