Half-integer

In mathematics, a half-integer is a number of the form $${\displaystyle n+{\tfrac {1}{2}},}$$ where ${\displaystyle n}$ is an integer. For example, $${\displaystyle 4{\tfrac {1}{2}},\quad 7/2,\quad -{\tfrac {13}{2}},\quad 8.5}$$ are all half-integers. The name "half-integer" is perhaps misleading, as each integer ${\displaystyle n}$ is itself half of the integer ${\displaystyle 2n}$. A name such as "integer-plus-half" may be more accurate, but while not literally true, "half integer" is the conventional term.^{[citation needed]} 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).^[1]