Lesson plan
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. 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).
Article summary
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. 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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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.