0, Zero, Cero, Zilch, Nada, Null, and Yes it has a History!

Zero, so simple it seems, but the truth is there is more to zero than meets the eye!

When I think zero, I first think of a number with no positive or negative value.  In the 7th grade mathematics class I am teacher assisting in, some students had difficulty figuring out which number system zero should be a part of.  The answer to this question is much more challenging than it seems at first.

Zero is considered to be a rational number because zero is considered to be an integer.  Zero is an integer though it is the only integer that is neither positive or negative. and 0 divided by any other integer equals zero.  Since a rational number is the quotient of two integers, zero can be considered a rational number.

Zero is a whole number also if you consider the definition of a whole number to include all nonnegative integers.  There are raging debates throughout the web on whether zero is a whole number or not.  A few fascinating ones can be found at the math forum and a physics forum.

Zero is a natural number depending on which definition of natural numbers you utilize.


or N∈{1,2,3,4,5,…}

So the answer to most questions related to zero is… that defining it is complicated.

Zero in my view is like a neutral number.  It is the break even point which separates above and below ground, above and below the sea.  The point at which a debt and a fortune are equal, so there is neither debt nor fortune.  Brahmagupta came up with the first rules regarding the concept of zero in the 7th century in India.  He said,

“When zero is added or subtracted from a number the number remains unchanged.”

He also established that anything multiplied by zero was equal to zero.

He viewed numbers as abstract entities, and this probably led to his contributions in defining the rules of zero.


There are many holes remaining in my definition of zero.  Zero is very difficult to define in one way.

The movie and book Holes.  Included a character named Zero.  It was said of Zero that he had nothing going on in his stupid little head.  That was the reason he was called Zero.  The reality was that the camp counselor that declared that did not fully understand zero.  Zero was a very smart kid, he just needed someone to believe in him!  Intriguingly the number zero is like this.  From a distant ignorant perspective the idea of zero seems pointless, but for those that view the bigger picture and get to understand zero the number is indispensable.

Zero from holes

Euler was certainly wiser than I, but there seems like a lot of mystery here!

“To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.” Leonhard Euler



  1. Nice post, and excellent Holes connection. Just a touch more for complete, to me: “but for those that view the bigger picture and get to understand zero the number is indispensable.” Why? What is it about zero that makes it irreplaceable? What issue(s) do you suppose Euler was talking about in his quote?
    clear, coherent, content, consolidated +


  2. I really liked reading your blog post. The connection you made with the movie and book of Holes was really interesting, and something I did not think about. It was nice to see how the word Zero is used in a different context outside of a math course. I think adding a little more history in your post would give it a little more credit ability on how tough of a subject zero really is.


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