Editing Half-integer (section)

{{Short description|Rational number equal to an integer plus 1/2}}
{{use dmy dates|date=February 2021}}
In [[mathematics]], a '''half-integer''' is a [[number]] of the form 
<math display=block>n + \tfrac{1}{2},</math>
where <math>n</math> is an integer. For example, 
<math display=block>4\tfrac12,\quad 7/2,\quad -\tfrac{13}{2},\quad 8.5</math>
are all ''half-integers''. The name "half-integer" is perhaps misleading, as each integer <math>n</math> is itself half of the integer <math>2n</math>. A name such as "integer-plus-half" may be more accurate, but while not literally true, "half integer" is the conventional term.{{citation needed|date=February 2020}} 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 integer]]s. For this reason, half-integers are also sometimes called '''half-odd-integers'''. Half-integers are a subset of the [[dyadic rational]]s (numbers produced by dividing an integer by a [[power of two]]).<ref>{{cite book |first=Malcolm |last=Sabin |year=2010 |title=Analysis and Design of Univariate Subdivision Schemes |volume=6 |series=Geometry and Computing |publisher=Springer |isbn=9783642136481 |page=51 |url=https://books.google.com/books?id=18UC7d7h0LQC&pg=PA51}}</ref>