Here’s another “debate” from the intense arena of mathematics. I use debate in quotes because there is one answer that is universally correct, and it’s just a matter of seeing the proof and choosing to accept it. It’s great that in math, most things are either 100% right or 100% wrong. This is one of those things.
Consider the following multiple choice question:
c.) all of the above
d.) none of the above
I’ll give you time to answer.
Okay, time’s up. Congratulations to all of you who said “A”. That is the right answer.
What you say? You want proof. Luckily I’m here to give you some proof. I wrote about 0.999… = 1 earlier, and then I linked to Wikipedia on the topic of zero in this post. And that Wikipedia article is fairly conclusive in the beginning assertion it makes in bold: The number 0 is even. And this appears occasionally on the ACT and SAT, so you may want to pay attention, or at least memorize the answer.
How could we tell if zero is even? Maybe we could analyze all the properties of even numbers, and see if zero fits in to any of them. Then, maybe we could analyze all the properties of odd numbers and see if zero fits into any of them. If zero fits into every property, it’s both even and odd. If it fits into none of the properties, it’s neither. If it fits into only the even properties, it’s even. Same for the odd properties.
The easiest definition in the book
We all know that even numbers are divisible by two, and thus return integers when divided by two. Odd numbers do not.
For example, 14 (an even number) divided by two is seven, which is an integer.
And 29 (an odd number) divided by two is 14.5, which is not a integer.
Zero divided by two is zero. Zero is an integer. This means zero is even.
Properties of Addition and Subtraction
- even number – even number = even number
- odd number – odd number = even
- even – odd = odd
- even + even = even
- odd + odd = even
- even + odd = odd
Well, for zero:
- 2 (even) – 2 (even) = 0
- 3 (odd) – 3 (odd) = 0
- -4 (even) + 4 (even) = 0
- -27 (odd) + 27 (odd) = 0
Therefore, zero fits exactly within the properties for even numbers. Additionally, it is impossible to construct a problem such that “even + odd = zero” or “even – odd = zero”. Therefore, zero doesn’t match any of the properties for odd numbers, either.
Properties of Multiplication
- even × even = even
- even × odd = even
- odd × odd = odd
Manipulating the properties of multiplication are far less conclusive, but it does make it clear that zero cannot be odd and odd alone.
If you define zero to be even, the problems are always true.
- 420 (even) × 0 (even) = 0 (even)
- 0 (even) × 613 (odd) = 0 (even)
If you define zero to be odd, the problems can’t prove zero to be odd alone.
However, if you’re going to define zero as “odd” or “both” (as done in the above example) then the previous properties, like even + odd = odd become false. 42 (even) + 0 (as an odd) = 42, which is not odd.
Properties of Splitting in Two
When an odd number is split into two groups, there is always one remaining.
Even numbers have no “odd one out”.
Similarly, zero split into two groups is hard to see. However, there is not a single dot that does not fit into one of the two groups. There is no “odd one out”, thus zero fits in the definition of an even number.
As you can see, there are two even groups on either side of the line.
Zero is even. Have fun on your next standardized test.
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