Zero – Mathematical Mysteries

Contents

Background

The word zero came into the English language via French zéro from the Italian zero, a contraction of the Venetian zevero form of Italian zefiro via ṣafira or ṣifr. In pre-Islamic time the word ṣifr (Arabic صفر) had the meaning “empty”. Sifr evolved to mean zero when it was used to translate śūnya (Sanskrit: शून्य) from India. The first known English use of zero was in 1598.

The Italian mathematician Fibonacci (c. 1170 – c. 1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, and was then contracted to zero in Venetian. The Italian word zefiro was already in existence (meaning “west wind” from Latin and Greek Zephyrus) and may have influenced the spelling when transcribing Arabic ṣifr. [1]

When did the concept of zero first appear in history?

The idea of zero appeared in stages, was not one invention, but two. The first zero was just a placeholder. Around 300 B.C., the Babylonians used two slanted wedges to mark an empty spot in a number, so they knew 2 2 was not 22. The Mayans independently created a similar placeholder.

But zero as a number you could calculate with was born in India. The oldest known use is a simple dot. Found in an ancient text called the Bakhshali manuscript–Now dated as early as the 3rd century.

The astronomer Brahma Gupta–Founded the rules for using it. He turned it from a mere symbol for nothing into a real number, the foundation of modern math.

OakTeller. “When did the concept of zero first appear in history?” 2025. Quora. Accessed July 7. https://qr.ae/pA3sRC.

Why don’t teachers want us to divide zero by zero? My math teacher just stopped and said, “Well, class, we’re changing the topic,” when I asked him.

I usually have a great time explaining this idea!

Why don’t teachers want us to divide zero by zero?

Division is the operation reciprocal to multiplication. So if I say 6 / 2 = 3, that means that 2 x 3 = 6.

So take any number other than zero and divide it by zero. Say 5 / 0 = X. If that is true, then 0 x X = 5. But there is no number that, when multiplied by zero, will equal 5. So N (where N is any number) / 0 is undefined because there is no answer to the reciprocal equation. X / 0 cannot be any number at all because 0 x (any number) can’t equal any number.

There is a special case, 0 / 0. Let’s say that 0 / 0 = Y. That means that 0 x Y = 0. That is true for any value Y. So, in this case, we can’t define 0 / 0 because 0 / 0 = (any number at all).

Why does x^0 = 1?

Why does zero factorial (0!) equal one (1)?

Factorial of a number in mathematics is the product of all the positive numbers less than or equal to a number.

Example: Factorial of n is n! and the value of n! is n!=n×(n−1)×(n−2)×…×1

The value of n! from the above can be also written as
n×(n−1)!
⇒n! = n × (n−1)!
Considering the value of n equal to 1,
⇒1! = 1! × (1−1)!
⇒1! = 1! × (0)!
The value of LHS should be equal to RHS as 1! is always equal to 1!
For the above condition to be true, the value of 0! must be equal to 1.
Therefore, the value of 0! =1.

Note: The factorial of a number is denoted by an exclamation mark. Factorial of a number only deals with natural numbers so zero is omitted. The multiplication of any factorial takes place down to 1 and not zero. Factorials are usually used in the context of solving permutations and combinations.

Who discovered zero (0)?

The concept of zero, as we understand it today, was developed over time in several different ancient cultures. The Babylonians had a placeholder concept similar to zero as early as 300 BC, but it wasn’t a separate numeral or a number with its own value.

The idea of zero as a number with its own value and as a placeholder in the positional number system was developed and refined in ancient India.

The concept is attributed to ancient Indian mathematicians around the 5th century AD, and the use of zero in these two fundamental ways transformed the numeral system. The mathematician Brahmagupta provided rules for mathematical operations like addition and subtraction using zero.

This Indian numerical system was brought to the Western world through the Arabs. In the Middle Ages, European mathematicians learned of it and adopted the so-called “Arabic numerals,” which included the use of zero.

Who invented the number zero?

Depends how you define “invented the number”. Aryabhatta utilized the concept of zero in his mathematical work, but he did not ascribe a symbol for it.

The oldest documentation of the actual symbol “0” and the origin of the word zero comes from the Persian al-Khwarizmi about 450 years later.

If we really want to give credit for the concept, we need to go back a hundred years before Aryabhatta to the Mayans or 700 years back to the Babylonians. Although, it is fair to say that our use of the concept comes from Aryabhatta.

The Invention Of Zero

Assigning Value To The Concept Of Nothing

This innate understanding for zero passes as common sense, yet it took thousands of years to develop a mathematical value to numerically represent it. While the concept is understood & applied to everyday life by the earliest humans, the written, numerical value of zero was only distinguished in relatively recent history. It’s obvious in hindsight, but think about the paradox involved here — we use numbers to represent value, yet, zero, or nothing, is inherently value-less.

Zero’s value is equivalent to the lack of value. An analogy here: zero is to math, as black is to color. Black is the lack of color, as zero is the lack of numerical value. Although black is the lack of color, it is still irrefutably a color. Applying this same principle to zero, the lack of a numerical value does not retract zero’s identity as a number.

Since zero does not exist in the natural world it is no surprise that it took thousands of years for civilization to conceptualize the numerical value of nothing.

Functionality was always understood, but the numerical quality of nothing has escaped the grasp of human comprehension until of recent. The concept of nothing has always been, yet it took the quantification of this nothingness to catalyze every aspect of modern life.

What is 1/0, 0/0 and 0^0?

I have put a lot of logical thought into this so I hope it is appreciated.

Is 0/0 undefined or indeterminate?

This topic fascinates people and is a constant cause of arguments!

I have a very readable explanation which I hope readers will appreciate!

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Here is a very interesting case!!!

Lloyd, Phillip. “Is 0/0 Undefined or Indeterminate?” 2025. Quora. Accessed July 7. https://qr.ae/pA3rpB.

Why do Whole Numbers Start from 0?

In summary, whole numbers start from 0 to create a comprehensive set encompassing the absence of quantity (0) and all positive integers. This inclusion of zero is fundamental for counting, mathematical operations, and providing a consistent and inclusive numerical representation in various mathematical contexts.

Why can’t you divide by zero? (TED-Ed)

In the world of math, many strange results are possible when we change the rules. But there’s one rule that most of us have been warned not to break: don’t divide by zero. How can the simple combination of an everyday number and a basic operation cause such problems?

[1] “0 – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/0.

[2] Lloyd, Philip. “Why don’t teachers want us to divide zero by zero? My math teacher just stopped and said, “Well, class, we’re changing the topic,” when I asked him.” 2023. Quora. https://qr.ae/prmsFF.

[3] Kemp, Sid. “Why don’t teachers want us to divide zero by zero? My math teacher just stopped and said, “Well, class, we’re changing the topic,” when I asked him.”. 2023. Quora. https://qr.ae/pys3DF.

[4] “Explain zero factorial”. 2023. vedantu.com. https://www.vedantu.com/question-answer/explain-zero-factorial-class-11-maths-cbse-6040d4d2bb704a431efe9b61.

a. “Why Does Zero Factorial (0!) Equal One (1)?”. 2023. Quora. https://qr.ae/pyMxM2.
b. “Zero Factorial: Why Does it Equal One?”. 2023. Statistics How To. https://www.statisticshowto.com/zero-factorial-why-does-it-equal-one/.
c. Davies, Joseph. “0! – What Is Zero-Factorial?”. 2023. zero-factorial.com. https://zero-factorial.com/whatis.html.

[5] Dijkhuizen, Bryan. “Who discovered zero (0)?”. 2023. Quora. https://qr.ae/pyeVqz.

[6] Frost, Robert. “Who invented the number zero?” 2023. Quora. https://qr.ae/pyeV3S.

[7] “The Invention Of Zero.” 2020. Setzeus. April 1. https://www.setzeus.com/community-blog-posts/the-invention-of-zero.

[8] Lloyd, Philip. “What Is 1/0, 0/0 And 0^0?”. 2023. Quora. https://qr.ae/pyZOCG.

[9] “Why Do Whole Numbers Start from 0?” 2024. GeeksforGeeks. February 16. https://www.geeksforgeeks.org/why-do-whole-numbers-start-from-0/.