The weighing pans of this balance scale
contain zero objects, divided into two equal groups.
is an even number. In other words, its parity
—the quality of an integer
being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer multiple
, specifically 0 × 2
. As a result, zero shares all the properties that characterize even numbers: for example, 0 is neighbored on both sides by odd numbers, any decimal integer has the same parity as its last digit—so, since 10 is even, 0 will be even, and if y
is even then y + x
has the same parity as x
and 0 + x
always have the same parity.
Zero also fits into the patterns formed by other even numbers. The parity rules of arithmetic, such as even − even = even
, require 0 to be even. Zero is the additive identity element
of the group
of even integers, and it is the starting case from which other even natural numbers
are recursively defined
. Applications of this recursion from graph theory
to computational geometry
rely on zero being even. Not only is 0 divisible by 2, it is divisible by every power of 2
, which is relevant to the binary numeral system
used by computers. In this sense, 0 is the "most even" number of all. (Full article...