Half-integer

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

n+{\tfrac {1}{2}},

where $n$ is a whole number. For example,

4{\tfrac {1}{2}},\quad 7/2,\quad -{\tfrac {13}{2}},\quad 8.5

are all half-integers. The name "half-integer" is perhaps misleading, 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 accurate, but even though not literally true, "half integer" is the conventional term. Half-integers occur frequently enough in mathematics and in quantum mechanics that a distinct term is convenient.

Note that 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 subset of the dyadic rationals (numbers produced by dividing an integer by a power of two).

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