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 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.
This number has only 2 positive divisors, itself and 1. What is it called?
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.
This is what you call numbers as you'd use them to count. Do you know what they're called?
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.
What do you call a number that is a part of a whole?
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!
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.
If you're counting out coins or buttons or peanuts, what kind of numbers are you using?
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.
Which of these numbers are defined as not being divisible by 2?
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.
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.
This term covers any number that describes or identifies something but doesn't hold that number's value. What is it?
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.
What kind of numbers are defined based only on the fact they're evenly divisible by 2?
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!
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
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.
What do you call a number that gives you a negative when you square it?
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.
Computers often use these numbers that have a base 16. What are they called?
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.
What do you call the kind of number you can get by dividing two integers?
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?
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.
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.
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.
What kind of number was invented by John Conway and Donald Knuth in 1974?
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.
Kurt Hensel first described these very complicated numbers in 1897. What are they?
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!
Any number made by multiplying two smaller integers qualifies as what?
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.
If something is a real number above zero, what is it?
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.
Which number is comprised of real and imaginary parts that are both 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."
What do you call a number if you can make a line segment representing it with a compass and ruler?
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.
This system is represented by 0s and 1s. What is it?
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.
Which kind of number cannot be written as a simple fraction?
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.
If a number can't be made simpler to remove a square root, what is it?
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.
When each number in a series is the sum of the two numbers before it, what would you call it?
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.