Parity of zero facts for kids
Parity of zero is the question whether the number zero is even or odd. Zero is even. Even numbers are defined to be integer multiples of two. That way, the numbers two, four and six are even, because they are one times two, two times two, and three times two. With that explanation, zero is also even, because it is zero times two.
Another explanation is from number theory: The integers are arranged in such a way that even numbers are followed by odd ones, and odd ones by even ones. Zero is preceded by minus one, and followed by one. Both numbers are odd. So it must be even.
Basic explanations
Given a set of objects, one uses a number to describe how many objects are in the set. Zero is the count of no objects; in more formal terms, it is the number of objects in the empty set. The concept of parity is used for making groups of two objects. If the objects in a set can be marked off into groups of two, with none left over, then the number of objects is even. If an object is left over, then the number of objects is odd. The empty set contains zero groups of two, and no object is left over from this grouping, so zero is even.
These ideas can be illustrated by drawing objects in pairs. It is difficult to depict zero groups of two, or to emphasize the nonexistence of a leftover object, so it helps to draw other groupings and to compare them with zero. For example, in the group of five objects, there are two pairs. More importantly, there is a leftover object, so 5 is odd. In the group of four objects, there is no leftover object, so 4 is even. In the group of just one object, there are no pairs, and there is a leftover object, so 1 is odd. In the group of zero objects, there is no leftover object, so 0 is even.
There is another concrete definition of evenness: if the objects in a set can be placed into two groups of equal size, then the number of objects is even. This definition is equivalent to the first one. Again, zero is even because the empty set can be divided into two groups of zero items each.
Numbers can also be visualized as points on a number line. When even and odd numbers are distinguished from each other, their pattern becomes obvious, especially if negative numbers are included:
The even and odd numbers alternate. Starting at any even number, counting up or down by twos reaches the other even numbers, and there is no reason to skip over zero.
See also
In Spanish: Paridad del cero para niños
