What is Division: Definition and 486 Discussions

A division is a large military unit or formation, usually consisting of between 6,000 and 25,000 soldiers.
In most armies, a division is composed of several regiments or brigades; in turn, several divisions typically make up a corps. Historically, the division has been the default combined arms unit capable of independent operations. Smaller combined arms units, such as the American regimental combat team (RCT) during World War II, were used when conditions favored them. In recent times, modern Western militaries have begun adopting the smaller brigade combat team (similar to the RCT) as the default combined arms unit, with the division they belong to being less important.
While the focus of this article is on army divisions, in naval usage, "division" has a completely different meaning, referring to either an administrative/functional sub-unit of a department (e.g., fire control division of the weapons department) aboard naval and coast guard ships, shore commands, and in naval aviation units (including navy, marine corps, and coast guard aviation), to a sub-unit of several ships within a flotilla or squadron, or to two or three sections of aircraft operating under a designated division leader. Some languages, like Russian, Serbian, Croatian and Polish, also use a similar word, divizion/divizijun/dywizjon, for a battalion-size artillery or cavalry unit.

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  1. G

    Generating division problems with integer results

    I'm not sure at all how best to approach this problem. Basically, the application is for practicing mental arithmetic. Most of the features are pretty easy, with the exception of division, which is the topic here. I accept a minimum and maximum for the first and last numbers in the division...
  2. J

    The upper division classes are not shown here, so wondering

    There must be about the same number of upper division classes for this engineering major as there are lower division? It would seem? Ok, so, this link shows lower division classes for the major, it does not show upper, so these are the classes for an engineering B.S. (In other words, these...
  3. E

    Evaluating Integrals Divisions for Physics Homework

    Homework Statement It's a physics problem, where i have to evaluate the root-mean-square radius defined by the expression below. (First for a constant \rho, then for a "(r)dependent" \rho).Homework Equations (\int{_0}{^\infty} \rho r^4 dr / \int{_0}{^\infty} \rho r^2 dr) ^(1/2)The Attempt at a...
  4. P

    Voltage Div. Homework: Find Voltage Drop Across 2K Ohm Resistor

    Homework Statement see attached for circuit from your result from part b, use voltage division to find the voltage drop across the 2k ohm resistor. my result from b was 250V part b question was voltage drop across 10K resistor Homework Equations The Attempt at a Solution R_T=5k...
  5. J

    Synthetic division with complex number

    I have been doing some homework on synthetic division today. Most of it is pretty straight forward, until I got to a problem with complex number I was able to solve the first problem (x^3 – 3x^2 + x – 3) / (x-i) By using +i for the ‘synthetic divisor constant’ (sorry don’t know the proper...
  6. K

    Proof of the Possibility of Division

    Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math...
  7. M

    Is the division of zero by zero a true division?

    Is it zero divided by zero even a division? According to some, it is not, because division would have three requirements: 1) That any quotient must be a number. 2) That any quotient multiplied by a divisor must give us a dividend, which presupposes that any quotient is a number. 3) That no...
  8. R

    Restoring and non restoring division algorithm

    Can anyone please explain to me how and why do restoring and non restoring algorithms for division work and please provide me with a correct flowchart for the non restoring division.
  9. T

    Time division multiplexing for analogue signal

    Hi guys, I am designing an OFDM system and then upconverted at 1 GHz. Now I have an idea of implementing TDM for this 1 GHz signal. Is it possible, please explain from theoretical point of view and if possible, please help from MATLAB perspective. Thank you very much,
  10. srfriggen

    Proof regarding division of integers

    Homework Statement Prove that for any a, b, c \inZ, if a l b (a divides b) and a does not divide c, then a does not divide b-c. Homework Equations The Attempt at a Solution Using the contrapositive: Prove that... if a l (b-c) then a does not divide b or a l c. 1. a l...
  11. I

    Limits: Division by 0, Making denominator = y

    Homework Statement So we have just been learning limits which I understand, however there was one example which completely through me. It was regarding division by 0. We had just been learning the known limits such as lim x->infinity (1/x) = 0 which I understood, and how anything similar such...
  12. M

    How Can I Solve This Division Problem?

    Homework Statement I added an attachment... I am not understanding how they did this...
  13. N

    MATLAB Simple matrix division in Matlab

    I have 2 matrices a=[1 2 3 4] and b=[1 4 9 16], i want to divide each term in matrix b by the same term in matrix a, in other words i want to end up with a matrix of [1 2 3 4]. Ive tried doing b/a, which clearly is wrong! Thanks for any help
  14. K

    Division Algorithm For Polynomials

    Im given two polynomials: f(x) =(2x^6) + (x^5) - (3x^4) + (4x^3) + (x^2) -1 and g(x)=(x^3)-(x^2)+2x+3 find polynomials Q(x),R(x) in the set of R[x] s.t f(x) =g(x)Q(X) +R(X) and deg(R)<deg(g) Am i even in the right area? and something to do with manipulating numbers in C[x]...
  15. X

    Exploring Division of s^4/(4s^4+1)

    Does it work ? Exp: (s power of 4) over (4 times s power of 4 plus 1) s^4 ---------- (4S^4)+1 LONG DIVISION : 1/4 _______ 4S^4+1√s^4...
  16. O

    Polynomial division proof

    Spivak's "Calculus," chapter 3 - problem 7 - a Homework Statement Prove that for any polynomial function f, and any number a, there is a polynomial function g, anad a number b, such that f(x) = (x - a)*g(x) + b for all x. (The idea is simply to divide (x - a) into f(x) by long division, until...
  17. B

    Division of Integers: Show n33-n Divisible by 15

    Homework Statement Show that for every integer n the number n33 - n is divisible by 15 Homework Equations The Attempt at a Solution Not sure what to do. I was thinking it might have something to do with both numbers are divisable by 3 ie the power = 3 x 11 and the divisor...
  18. Z

    Rules behind this type of division?

    I know this is a silly question for a 12th grader to ask but I don't know the exact rules. If we divide 950 by 121, the first digit of quotient is 7, then we place a decimal after 7 and bring one 0 down, which is correct way. In the division of 21780/704, the first digit of quotient is 3...
  19. M

    Are There Other Strange Division Patterns Besides Cancelling 6's?

    Homework Statement how come that 16/64=.25 166/664=.25 1666/6664=.25 and any 1then n number of sixes / the same number of sixes then 4 = .25 same thing with 19 / 95 is there other strange division patterns?
  20. B

    Abstract Algebra, Division Ring question

    Homework Statement Let R = { [ a + b*sqrt(m) c + d*sqrt(m) ] } [ n(c - d*sqrt(m)) a - b*sqrt(m) ] (Sorry if the matrix is unclear... I can't get it space nicely. r11 = a + b*sqrt(m) r12 = c + d*sqrt(m) r21 = n(c -d*sqrt(m))...
  21. L

    Understanding Photodivision and Electrodivision in Electron Beam Oncology

    Im reading a paper about use of electron beams in oncology and it says: "The mechanism of neutron production in the region of electron beam energies under consideration is determined by photodivision of nuclei by bremsstrahlung photons and the small contribution of electrodivision by...
  22. C

    Are Upper Division Physics Classes Inspiring?

    Hi. I'm a second year physics and astronomy major. I'm beginning to worry that I have entered these two majors with unrealistic expectations. The problem is that I developed my passion for physics throughout high school by reading popular science books like The Elegant Universe and Many...
  23. W

    Cake Division Puzzle: Max Amount for 1st Person

    Homework Statement Suppose that two people are dividing two cakes using the following rules: 1. The first person divides the first cake into two pieces in any fashion. 2. The second person then chooses which of the two cakes they will get to choose the first piece from. 3. The first person...
  24. B

    Normed division algebras: geometrical limitation

    For some time I've been trying to get a geometric appreciation of why normed division algebras only exist in dimensions 1,2,4,8 (namely R,C,H,O). As always Baez provides the most elegant answer: http://math.ucr.edu/home/baez/octonions/node6.html" Allow me to descibe the key point of the...
  25. G

    What is the result of dividing log(log x) by log x?

    what is: [log(log x)] / [log x]i would guess logx/1 but not sure
  26. E

    Fourier Division Algorithm Explained

    There is an article on wikipedia (http://en.wikipedia.org/wiki/Fourier_division" ) about Fourier division algorithm, but there is something that confuses me. When they compute the so called "b terms" they have to divide 2 numbers. Let's call them x and y, and x/y=q+r. To compute q and r they use...
  27. J

    Least positive rest in division?

    Homework Statement Find the least positive rest in division of 7^35 with 5 Homework Equations (7^35)/5 The Attempt at a Solution 7^35=378818692265664781682717625943 => 378818692265664781682717625943/5... Uhhhhh this is not the way I am supposed to take right? :cry:
  28. J

    Vector division or inversion

    How do you get a vector to the power of negative one? I.E. : V ^ (-1)? Or inversion if that's what it's called? Thank you.
  29. A

    Measurable functions and division by zero

    Consider the function g(t) = f(t)/t on [0,1], where f is measurable on [0,1]. Does it follow that g is measurable on [0,1]? I know there's a problem -- namely, division by zero -- only on a set of measure zero -- namely, \{0\} -- and that g agrees with the measurable function g_0 = g|_{(0,1]}...
  30. A

    Why is division not a viable operation for vectors?

    Why division is not possible between vectors? We have seen in many books that there is vector addition, subtraction and multiplication .. but division between two vectors or more vectors is not anywhere... what is the reason of not having division in vectors.does it have any connection with...
  31. S

    How Does the Mitotic Spindle Influence Organelle Division During Cell Mitosis?

    Hello everyone, When a cell divide, do the organalles divide, or does DNA divide first, and using that DNA information new cells synthesize organalles. Thanks :smile:
  32. S

    How does inhibting bacterial protein synthesis inhibit bacterial division?

    Hello everyone, Quick question. I can understand proteins are needed to make everything in the cell, so if you inhibit bacterial protein synthesis, cell division can not occur. However my question is does the DNA replicate and divide, and then the cell can not make other things they want so...
  33. U

    Beginner's Question Regarding Voltage Division

    I'm pretty much a beginner trying to wrap my head around the concept of voltage division within a circuit. To help myself out, I've come up with the following circuit. [PLAIN]http://img401.imageshack.us/img401/801/voltagedivision.gif I am having trouble determining the voltage between...
  34. S

    Division algorithm in A[x] (A NOT a field)

    is it possible? I'm reading a proof where A is a local ring and f is a monic polynomial, v another polynomial in A[x] then the author says there is q,r with v=qf+r and degf<r. I thought the algorithm required divison of coefficients?! Maybe it's true we can always do this with f monic? thanks
  35. T

    Understanding Voltage Division in Circuits: A Superposition Approach

    Homework Statement Calculate v (refer to attachment). Homework Equations Voltage division: Vout = Vin x R2 / R1 + R2 The Attempt at a Solution V1 = V1 x R2 / R1 + R2 = 15 x 5 / 10 + 5 = 5V V2 = V2 x R4 / R3 + R4 = 5 x 2 / 10 + 2 = 0.83V V = 5 + 0.83...
  36. X

    Proving Division of Local Ring in Ring with Idempotents

    Let R be a ring . Suppose that e and f=1-e are two idempotent elements of R and we have R=eRe \oplus fRf (direct sum ) and R doesn't have any non-trivial nilpotent element . Set R_1=eRe and R_2=fRf . If R_1=\{0,e\} and R_2 is a local ring , then prove that R_2 is a division ring . (note that e...
  37. D

    Division Algorithm: 15÷29=0 R15 Linear Equation

    Find the quotient and the remainder when 15 is divided by 29. Use the division algorithm to write your answer as a linear equation (i.e., use the division algorithm to write 15 divided by 29 as a linear equation) I wrote 15=29*0+15 but this problem was marked wrong when I submitted it...
  38. C

    Prime division & repetition period

    Something odd i noticed while playing around with primes. We have the set of prime numbers P and a p ∈ P. Define a function f:Q → N that will give the period of the repetition in the decimal expansion of some number r ∈ Q. 1) ∀ p ∈ P: ∃ n ∈ N: ∀ q ∈ P, q < p: f(q/p) = n. So n is...
  39. J

    How Do I Solve Polynomial Division and Trigonometric Identities?

    Homework Statement I forgot how to divide this 1.) x^2 + 15 -8x divided by 3 - x I don't know how to start since 3 has nothing to do with x^2. The result from the book is 5 - x. I also don't understand this problem which uses trigonometric identities. if x = a sin theta then...
  40. S

    Summation of the polynomial and division

    Homework Statement Let p(z) = \sum_{j=0}^{n} a_{n-j}z^j be a polynomial of at least degree 1 thus n \geq 1. Show that if z\neq 0 then 1/z is a root of the polynomial p. Homework Equations Fundamental theorem of Algebra The Attempt at a Solution If a expand the polynomial...
  41. F

    Long division to solve indefinite integral

    Homework Statement how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx Homework Equations using long division The Attempt at a Solution x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure
  42. C

    Polynomial Division: Show g(x) Divides f(x)

    Homework Statement Show that g(x) = x^3 + 1 divides f(x) = x^{9999} +1. Homework Equations The Attempt at a Solution g(x) can obviously be factored into the irreducible polynomials (x+1)(x^2 - x + 1) in Z[x], and since f(-1) = (-1)^{9999} + 1 = 0, the factor theorem gives that (x+1) divides...
  43. K

    Proving R is a Division Ring or Has Prime #Elements

    Homework Statement Problem 3.5.2 Let R be a ring such that the only right ideals of R are (0) and R. Prove that either R is a division ring or that R is ring with a prime number of elements in which ab = 0 for every a, b \in R. Homework Equations The Attempt at a Solution...
  44. S

    How is integration of a division done with partial fractions?

    This has been posted in another, but the wrong, section of the forum. That's why there are already quotes in it. Hello, Homework Statement I don't understand a step in the following integral: ∫(x-1)/(2x+1)dx = ∫(1/2)dx − (3/2)∫1/(2x+1)dx = (1/2)x − (3/4)ln|2x+1| + C The first...
  45. N

    Disc. math/logic: division & modulus proofs

    Homework Statement Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd. Let m be a positive integer. Show that a mod m = b mod m if a ≡ b(mod m) Homework Equations | means "divides," so a | b means "a divides b" or "b can be divided by a" mod gets the...
  46. K

    Division algorithm for polynomials

    Homework Statement M and N are positive integers with M>N. The division algorithm for integers tells us there exists integers Q and R such that M=QN+R with 0\leqR<N. The division algorithm for real polynomials tells us that there exist real polynomials q and r such that xM - 1 = q(xN - 1) +...
  47. T

    Division with the rectangular form

    Hi everyone, I was questionning myself about a problem that I have surely learn in school but I want to know if it's possible to solve a division with imaginary numbers without using the polar transformation. Example: \frac{2+2i}{1-i} So with the polar tansformation we have...
  48. J

    Why does the definition of cosh and sinh contain division by 2?

    cosh = \frac{e^x + e^{-x}}{2} In the above definition, why there is division by 2? Is it there so that when x=0, y could be 1?
  49. J

    Understanding the Tyco Electronics Multimode Relay MT (Schrack Division)

    I am currently looking at a Tyco Electronics Multimode Relay MT. (Schrack division). I am wondering what it means in the description when it mentions CO contact configuration.
  50. D

    Questions about proof of the division article.

    (Thread should be named: Question about proof of the division algorithm, sorry about that) Hi, I am reading this proof of the division article: http://xmlearning.maths.ed.ac.uk/lecture_notes/polynomials/division_algorithm/division_algorithm.php" I will write some of it here in case you don't...
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