half-integer

In mathematics, a half-integer is a number of the form n + \tfrac{1}{2}, where n is an integer. For example, 4\tfrac12,\quad 7/2,\quad -\tfrac{13}{2},\quad 8.5 are all half-integers. The name "half-integer" is perhaps misleading, as each integer n is itself half of the integer 2n. A name such as "integer-plus-half" may be more accurate, but while 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).