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| | Greetings! I am Marvella and I really feel comfortable when individuals use the complete title. I am a meter reader. What I love doing is to gather badges but I've been taking on new issues lately. North Dakota is where me and my spouse reside.<br><br>Here is my web-site; [http://Tomjones1190.livejournal.com/ healthy meals delivered] |
| In [[mathematics]], a '''half-integer''' is a [[number]] of the form
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| :<math>n + {1\over 2}</math>,
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| where <math>n</math> is an [[integer]]. For example,
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| :4½, 7/2, −13/2, 8.5
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| are all half-integers. Note that a half of an integer is not always a half-integer: half of an [[even integer]] is an integer but not a half-integer. The half-integers are precisely those numbers that are half of an [[odd integer]].
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| The [[Set (mathematics)|set]] of all half-integers is often denoted
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| :<math>\mathbb Z + {1\over 2}.</math>
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| ==Uses==
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| Half-integers occur frequently enough in mathematical contexts that a special term for them is convenient. For example, the densest [[lattice packing]] of unit [[sphere]]s in four dimensions places a sphere at every point whose coordinates are either all integers or all half-integers; this packing is closely related to the [[Hurwitz integer]]s, which are [[quaternion]]s whose real coefficients are either all integers or all half-integers.
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| Moreover, the [[Pauli exclusion principle]] results from definition of [[fermion]]s as particles which have [[spin (physics)|spin]]s that are half-integers. The [[energy level]]s of the [[quantum harmonic oscillator]] occur at half-integers and thus its lowest energy is not zero.
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| Also, the [[factorial]] and [[gamma function]]s, while not defined for [[negative number|negative and non-positive integers]] respectively, are defined for all half-integers as rational multiples of the [[square root]] of [[pi]].
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| [[Category:Rational numbers]]
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| [[Category:Elementary number theory]]
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| [[Category:Parity]]
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Greetings! I am Marvella and I really feel comfortable when individuals use the complete title. I am a meter reader. What I love doing is to gather badges but I've been taking on new issues lately. North Dakota is where me and my spouse reside.
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