The number 0 has a very important, and even central role in mathematics, both today and even centuries ago. Zero, apart from being a number, is also a numerical digit that represents that number in a numeral system. Of course, there are plenty of numeral systems, and while they have different digits and characters, the value of that number is the exact same we know and use. There are have been many names for the number 0 over the years, and some of them stayed and can be found in use even to this day. We’ll discuss that right away, and then you’ll have an easy time with understanding what is 0.
Origin of the word
The road to arriving at a name ‘zero’ was long, and it was passed down from a few languages. There are plenty of mentions of the words, but it’s known that it originates first from Italian “zefiro” or “safira or sifr” and had a meaning of “empty or nothing”. There were some additional Indian influences from the word “sunya”. Additionally, it is well-known that Fibonacci, who lived in the 12th and 13th century and grew up in North Africa, after introducing the decimal system to Europe called the number 0 “zephyrum”. In the end, zero was taken from French, and the first documented use of the word was found to be in 1598.
Zero in language
There are multiple common names we use in English – nought and naught in the United Kingdom and the United States, respectively, as well as nil and zilch or zip in some cases. When it’s clear that it’s not a letter O, o or oh can be used in conversations too. Furthermore, the concept of zero – none or nothing, can be called nada, or scratch, or even duck egg and a goose egg in slang, although rarely heard.
Zero in mathematics
Of course, 0 is a central concept of mathematics and is an integer preceding 1 immediately. Just a reminder – integers are numbers that can be written without a fractional component. It’s also a natural number and the only one that isn’t positive because 0 is neither negative nor positive. The number 0 also means a count of null size, which is a concept known in most cultures today.
Parity of zero
When it comes to the parity of zero – zero is an even number, because it can be divided by 2 without a remainder. Additionally, it shares all properties of even numbers – it’s neighbored by odd numbers on both sides. Also, by a rule that any decimal integer possesses the same parity as its last digit – by using an example of 10 which is an even number too. If you decide to subtract an even number by an even number, the result is always an even number, which further proves this point. Even though it seems logical and easy, a lot of students struggled with an answer to this question, studies have shown.
Use of zero in elementary algebra
It’s actually the smallest non-negative integer, with no natural numbers preceding 0, and the following one is, of course, 1. Zero is not a natural number, but it’s a whole number, a rational and a real number. It’s also the central number on the number line. 0 also isn’t a prime or composite number – prime numbers are those that can be formed by a multiplication of two smaller natural numbers, like 2, 3, 5, 7, 11, etc. Composite numbers are natural numbers greater than 1 that aren’t prime, obviously – 4, 6, 8, 9, etc.
Here are some basic rules that you should be familiar with from elementary school, which are meant as a reminder – it’d be a shame if you didn’t know them already. The number x can be any real or complex numbers.
- Subtraction: x – 0 = x also 0 – x = -x
- Addition: x + 0 = 0 + x = x
- Division: 0 / x = 0, if x isn’t zero. x/0 is undefined because no number multiplied by 0 produces 1.
- Multiplication: x · 0 = 0 · x = 0
- Exponentiation: x^0 = x / x = 1, if x = 0, it’s undefined. if x is positive and a real number, 0^x = 0
- The sum of 0 numbers is 0 (empty sum), but the product of 0 numbers is 1 (empty product).
- Factorial of 0: 0! = 1
Zero used in simple functions
Functions are recognized as more complex uses of zero, usually taught in high school and college, and have to do with functions and domains, but they’re equally important.
For example, If we take a function f, the zero of the function is a point x, and in the domain of the function when f(x) = 0. It sounds way more complicated than it really is, and is evident once you draw a picture. If there are a finite number of zeros – they’re called roots of the function. Zero function or zero map, on the other hand, in a domain D is a constant function where 0 is the only possible output value. That means f is defined by f(x) = 0 for any possible x in the domain. Furthermore, the zero function is the only function that is both even and odd.
The use of zero in other fields
- In physics, the zero level is distinguished from all other levels – for absolute temperature measured in Kelvins, zero is the lowest possible value. Even though negative temperatures exist, they’re not actually colder. If we measure temperature in Celsius, the 0 is the freezing point of water. If we measure sound intensity in decibels, zero level is a reference value. In many systems, 0 is the energy of the ground state of the system which means a system independent of time.
- When using a telephone, pressing 0 means you’re probably going to dial a number out of the company network, which means calling abroad, to another region.
- If you’re playing roulette, there is a space called “0” or “00”, and the presence of that space is ignored, which is fitting.
- You should be aware of this – but on the Interstate Highway System in the United States, exits are numbered with the nearest milepost in regard to state borders. If the distance to a state border is less than half a mile, which is approximately 800 meters, the exit is numbered as Exit 0.
It’s obvious where the number 0 came from – from a need for people to somehow mark the concept of nothingness or non-existence. The history of zero dates back millennia, and there were findings in Ancient Egyptian culture, Maya numerals used a zero, Ancient Greeks did so too, as well as other eastern cultures like India and China and Arabic-speaking countries. The zero reached Europe from those countries around the 11th century, and it later became the zero we know today. It’s irrefutable how much influence it had in numerical systems of other countries, and the fields of mathematics are definitely enriched for the existence of one simple number – 0.