integer

integer : The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French) are natural numbers including 0 ( 0, 1, 2, 3, ...) and their negatives (0, −1, −2, −3, ...). They are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers. In other terms, integers are the numbers one can count with items such as apples or fingers, and their negatives, as well as 0. More formally, the integers are the only integral domain whose positive elements are well-ordered, and in which order is preserved by addition. In algebraic number theory, these commonly understood integers, embedded in the field of rational numbers, are referred to as rational integers to distinguish them from the more broadly defined algebraic integers. Like the natural numbers, Z is closed..   More from Wikipedia

integer : In mathematics, Eisenstein integers, named after Ferdinand Eisenstein, are complex numbers of the form where a and b are integers and is a complex cube root of unity. The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers which..   More from Wikipedia

integer : A quantum computer is any device for computation that makes direct use of distinctively quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. See also: Matter & Energy Quantum Physics Quantum Computing Physics Computers & Math Quantum Computers Hacking Information Technology In a classical (or conventional) computer, information is stored as bits; in a quantum computer, it is stored as qubits (quantum bits). The basic principle of quantum computation is that the quantum properties can be used to represent and structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Although quantum computing is still in its infancy, experiments have been carried out in which quantum computational operations were executed on a very small number of qubits. Research in both theoretical and practical areas continues at a frantic pace, and many national government and military funding agencies support quantum co....   More from Science Daily

integer : The neutrino is an elementary particle. See also: Space & Time Astronomy Cosmic Rays Matter & Energy Quantum Physics Physics Optics It has half-integer spin and is therefore a fermion. All neutrinos observed to date have left-handed chirality. Although they had been considered massless for many years, recent experiments have shown their mass to be non-zero. Because it is an electrically neutral lepton, the neutrino interacts neither by way of the strong nor the electromagnetic force, but only through the weak force and gravity. Because the cross section in weak nuclear interactions is very small, neutrinos can pass through matter almost unhindered. For typical neutrinos produced in the sun (with energies of a few MeV), it would take approximately one light year of lead to block half of them. Detection of neutrinos is therefore challenging, requiring large detection volumes or high intensity artificial neutrino beams. There are three known types (flavors) of neutrinos: electron neutrino....   More from Science Daily

  WEBSITE: www.teachertube.com 11609Consecutive Integer Problems Day 2

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Question : I'm going to be tested on the sets of numbers, and I was wondering if either a square root or a fraction which can simplify to an integer is considered an integer. For example, is square root 9 an integer? Is 8/2 an integer?

Answer : When you try to decide what kind of a number it is, you always simplify it first. So, any thing that can be simplified into an integer is considered an integer...   More from Yahoo Answers

Question : Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. P has degree 2, and zeros 1 + i 5 and 1 - i 5. P(x) =?

Answer : If x = a is a zero, then x - a is a factor. Since x = 1 + i 5 and x = 1 - i 5 are solutions, we have the following equation for P(x): P(x) = [x - (1 + i 5)][x - (1 - 5)] ==> P(x) = (x - 1 - i 5)(x - 1 + i 5) You can re-write this and get: P(x) = [(x - 1) + i 5][(x - 1) - i 5] This is a difference of squares, so we can get: P(x) = (x - 1) - (i 5) ==> P(x) = x - 2x + 1 - i (5) ==> P(x) = x - 2x + 1 - (-1)(5) ==> P(x) = x - 2x + 1 + 5 ==> P(x) = x - 2x + 6 Answer Verification: http://www.wolframalpha.com/input/?i=x%C2%B2+-+2x+%2B+6 I hope that helps!..   More from Yahoo Answers

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