Skip to content

On the Classification of Zero

Nov 10, 2007
tags: , , ,

I was surprised when one student approached me and asked this question:

Is zero odd or even?

Come on guys, was there ever a doubt? Zero is an EVEN number.

We can classify integers into two types: odd or even. By definition, an even integer is divisible by 2, which means that when you divide it by two, you get an integer quotient. No remainders, no fractions, no annoying numbers after the decimal point. Anything that is not even will be classified as an odd integer. Another definition of an even number is that you can write that number as 2*k, where k is an arbitrary integer. In fact, when I was in grade school, I was taught that a number that ends in 0, 2, 4, 6 or 8 is even. Of course, with this definition, there is no sense trying to classify non-integers as odd or even.

Now let’s look at the number zero. What happens when you divide it by two? You get zero, which is an INTEGER. Therefore, it is even. In fact you can write zero as 2*0, which is of the form 2*k with k = 0. And since you only have one digit, then zero ends with 0. Conclusion: zero is even.

Maybe some students get it confused with another concept. Zero is NEITHER prime nor composite. Just like the number one.

Now, if you are talking of functions, then we have an entirely different classification. The zero function is BOTH an even function and an odd function. Recall the definition of odd and even functions, and you will discover that the zero function will satisfy both definitions.

[I posted this entry months ago in my other blogs, but I realized that it is appropriate to include this entry here.]

Advertisements
One Comment leave one →
  1. Nov 12, 2007 5:53 am

    One of my students asked me the same question recently! Conclusion – students are similar all over the world! 😀

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: