Why is Zero an even number?

<8.7 Why is Zero an even number? | Topic Index | 9.1 Arithmetic Operation Metaphors >

As long as we were dealing with natural numbers, we used the imagery of sharing or pairing objects to understand the idea of odd & even numbers.

When 0 was invented, the set of natural numbers became the set of Whole Numbers.

The question arose whether 0 is an odd or even number.

But 0 is not a quantity. It indicates absence of a quantity.

Hence, we cannot use the imagery of a collection of objects to decide this question.

But by studying the property of odd & even, we had observed some patterns.

We need to use the logic of arithmetic, and extend these patterns to decide this question.

After many discussions, 0 was considered an even number. There are three ways to justify this.

1. In arithmetic, the idea of sharing in 2 equal parts is represented by the idea of dividing by 2 and 0 is divisible by 2. Hence 0 is an even number.

2. 0 + odd = odd & 0 + even = even because adding by 0 does not change a number. These equations would be true only if 0 is considered even.

3. One more than 0 is 1 which is odd. Two more than 0 is 2 which is even. Hence 0 is an even number.

This is an example of the power of arithmetic for answering questions about things which may not even exist in real life!