half-integer

 In mathematics, a half-integer is a number of the form

${\displaystyle n+{1 \over 2}}$,

where ${\displaystyle n}$ is an integer. For example,

4​¹⁄₂, 7/2, −13/2, 8.5

are all half-integers. Half-integer is perhaps a misnomer, as the set may be misunderstood to include numbers such as 1 (being half the integer 2). A name such as "integer-plus-half" may be more representative, but "half integer" is the traditional term.^{[citation needed]} Half-integers occur frequently enough in mathematics that a distinct term is convenient.

Note that a halving an integer does not always produce a half-integer; this is only true for odd integers. For this reason, half-integers are also sometimes called half-odd-integers. Half-integers are a special case of the dyadic rationals (numbers produced by dividing an integer by a power of two).^[1]

Notation and algebraic structureEdit

The set of all half-integers is often denoted

${\displaystyle \mathbb {Z} +{1 \over 2}.}$

The integers and half-integers together form a group under the addition operation, which may be denoted^[2]

${\displaystyle {\frac {1}{2}}\mathbb {Z} }$.

However, these numbers do not form a ring because the product of two half-integers cannot be itself a half-integer.

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.