Information AboutHalf-integer |
| CATEGORIES ABOUT HALF-INTEGER | |
| rational numbers | |
| elementary number theory | |
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In Mathematics , a half-integer is a Number of the form , where is an Integer . For example, 3/2, 7/2, -13/2 are all half-integers. Note that a half of an integer is not always a half-integer. For example, half of an Even Integer is an integer but not a half-integer. The half-integers are precisely those numbers which are half of an Odd Integer . The Set of all half-integers is often denoted . Half-integers occur frequently enough in mathematical contexts that a special name 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. Moreover, the Pauli Exclusion Principle results from definition of Fermion s as particles which have 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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