On the Classification of Zero

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.]

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