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. S

    B Remainder when the dividend is less than the divisor

    I am Sorry it's a silly question but its been bothering me, So I needed to ask... In the process of division, when there is a condition like- 4/5 when the divisor is greater then the dividend. why is the Remainder 4 ? as when the divisor is greater then the dividend then the division goes in...
  2. paulb203

    B Why are the division rules for surds the way they are?

    Why does, 4√64÷2√4 =2√16 ? I can see the method (4÷2=2, √64÷√4=√16) But why is it not; 4 times √64 divided by 2 times √4 (as per BODMAS) i.e, 4 times 8 divided by 2 times 2, which = 32 Nb. When I put it into my calculator that way it gives 32 as the answer (4*√64÷2√4)
  3. N

    B 1 divided by infinity equals zero (always?)

    I understand the mathematics that 1 divided by infinity is virtually zero and so equals zero. I look on the internet and that is the answer that I get. Is this a simplification for early mathematics learning and, if I continue, will I find a more complex answer? The reason that I ask is that I...
  4. M

    B Relation between Division and multiplication

    For example what is ##\frac {169}{13} = ?## This says “When ##169## is divided into ##13## groups how many there are in each group?” This can be converted into a multiplication problem like this “##13## groups of how many in each group makes ##169##?” This is ##13 * ? = 169##. It can be solved...
  5. A

    B Confusion about division by zero in sets

    So the confusion here is that division by zero is often said to be undefined. So whereas, the point (0,0) certainly appears in the set of values where x=y, does the point (0,0) appear in the set of values where 1=y/x. Why or why not? In other words are the set of points where x=y the same as...
  6. AtoMick-u235

    Why does a division by zero produce an error or undefined message?

    A division by zero is a mathematical oddity, , if a computer or calculator etc performs a 1\0 they would crash, the OS prevents the execution, and displays ERROR or UNDEFINED, , , some versions of windows calculator display positive or negative infinity, , try it Any ideas on this ?
  7. S

    Comp Sci 8 bit block division -- University Level Intro Course: Networking

    What I think I should do: 1 = 0001 7 = 0111 3 = 0011 First block = 00010111 Second Block = 00110000 Now, I do binary division 00010111/11010 = find the answer 00110000/11010 = find the answer This is what I think I should do, but I am not sure if this is correct. Is this basically CRC? Any...
  8. drooble122

    Method of detached coefficients division

    -1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5 1 2 -3 7 9 -31 15 7 14 -21 -5 -10 15 5 -10 15The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be...
  9. AryaKimiaghalam

    Why isn't Geophysics a division of the APS?

    Curious to know why...
  10. 1

    Calculate ways to form a committee of 3 from 8, without division?

    I grok, am NOT asking about, the answers below. Rather, how can I calculate the final answer DIRECTLY, without division? I don't know why my Latex isn't rendering here? Please see: [web link redacted by the Mentors] Orange underline 1. Unquestionably, $\color{#FFA500}{4 \times 3/2} = 3!$ But...
  11. karush

    MHB -c11.interpretation of division

    Consider the division problem $\dfrac{99}{33}$ a. Which interpretation do you think would be easier to use if you need to draw a picture? $\circ \quad$ partitioning equal subsets $\circ \quad$ repeated subs traction ok I tried to look up some definitions for this question but didnt see how it...
  12. karush

    MHB 07 division by doubling method

    use doubling method $\dfrac{972}{69}$ $1 \to \boxed{69}+\boxed{a}=\boxed{?}$ $2 \to \boxed{138}+\boxed{b}=\boxed{?}$ is a 100 then what is b?
  13. karush

    MHB 04 scaffold partial products for division

    ok obviously easy but I never heard of the terminology for division a friend sent me this screen shot so I don't know the explanation given it seem more complicated than it needs to be Anyway Mahalo if you are familiar with this
  14. C

    Simple Induction Induction proof of Polynomial Division Theorem

    Theorem: Let ## f(x), g(x) \in \mathbb{F}[ x] ## by polynomials, s.t. the degree of ## g(x) ## is at least ## 1 ##. Then: there are polynomials ## q(x), r(x) \in \mathbb{F}[ x] ## s.t. 1. ## f(x)=q(x) \cdot g(x)+r(x) ## or 2. the degree of ## r(x) ## is less than the degree of ## g(x) ## Proof...
  15. E

    MHB Indefinite integral in division form

    I have the following integration - $$\int \frac{2}{x - b \frac{x^{m - n + 1}}{(-x + 1)^m}} \, dx $$ To solve this I did the following - $$\int \frac{1 - b \frac{x^{m - n}}{(-x + 1)^m}+1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx $$ Which gives me -...
  16. S

    I How to visualize division in the Odds form of Bayes's Theorem?

    Here I'm asking solely about the circle pictograms. Please eschew referring to, or using, numbers as much as possible. Please explain using solely the circle pictograms. Undeniably, I'm NOT asking about how to divide numbers. I don't understand 1. How do I "visually" divide Circle 1...
  17. S

    MHB How to visualize division in the Odds form of Bayes's Theorem?

    I saw this question at https://math.codidact.com/posts/283253.
  18. karush

    MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?

    Use factor theorem and syntheitc division and its conjugate to decide whether the second polynomial is a factor of the first $x^3-5x^2+3x+1;\quad x+1$ \item \textit{apply synthetic division} \item$\begin{array}{c|rrrrr} 1 &1 &-5 &3 &1\\ & &1 &-4 &-1\\ \hline &1 &-4 &-1 &0...
  19. IDontHaveAName

    Admissions Having an A- average in upper division physics course

    Hello, all I'm a rising senior who's about to apply for grad school. However, this year has been a rough year for me as my overall grade has declined a bit, especially in that I did not do well in 3 core major courses: mechanics B and EM II I got a B and STAT MECH B+(sadly, I thought i deserved...
  20. H

    Understanding the Current Division Rule: A Circuit Diagram Guide

    Here's the diagram of the circuit: And here's the solution I found on a site on Google: I tried to follow through the solution given, but can't understand how it is applying current division rule to find current in QA and QB, and subtracting current values to find the current in AB is still...
  21. S

    Remainder of polynomial division

    ##x^{2017} + 1 = Q(x) . (x-1)^2 + ax + b## where ##Q(x)## is the quotient and ##ax+b## is the remainder ##x=1 \rightarrow 2 =a+b## Then how to proceed? Thanks
  22. curiosissimo

    Using Kirchhoff's laws on this current division problem

    The main problem is the verse of the 2 currents ## i1 ## and ## i2 ## . I think they both go clockwise, so in the node A we should have ##i1+i2=20A##. Now let's apply the second law (going clockwise). So ##ΔV1-R1*i3 - R2*i4 + ΔV2=0##, where ##i3## and ##i4## are the currents which pass through...
  23. penroseandpaper

    Group theory with addition, multiplication and division

    Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...
  24. chriscarson

    "To the power of" (powers in division have to be subtracted)

    Our teacher said that powers in division have to be subtracted when the same base , but still , I am not getting the right answer.
  25. akashpandey

    I Division of a physical quantity

    As we all know that division simply means how many parts of the whole we have (or splitting into equal parts) 1)Example:- if we have 12 apples and there are 3 people so each will get 4 apples right. Easy! Now my question is how does this definition makes sense in term of physical quantities ...
  26. Y

    MHB Is a Number Divisible by 15 and 18 Also Divisible by 27?

    Hello, I got a very basic question... A number n is dividable by 15 and 18. Can I assume from that that it is dividable by 27? (dividable - you can divide it by 15 and get no reminder). If it is dividable by 15, it is by 3 and 5. If by 18, it is dividable by 3 and 6, which means 3 and 2...
  27. Ethan Klein

    Courses Course Order For Upper Division

    I'm curious if anyone has either shared a similar experience or has input regarding this. I was planning to take Stat Mech my second semester junior year, but heard the prof is AWFUL and unorganized, so I signed up for solid state instead (upon hearing that the solid state prof is awesome). My...
  28. B

    What are the rules for argument division in complex numbers?

    above video states that arg(z1/z2) = arg(z1) - arg(z2) this is seems very similar to Log rules but these are inverse function for angles right? And log rules only apply to logarithms, not sure where he got this from? What am i missing?
  29. K

    Other Upper division undergraduate electronics and circuits textbooks

    Hello everyone, I am in an upper division undergraduate electronics and circuits class right now and the textbook that were using (Eggleston: basic electronics for scientists and engineers) is not resonating with me. I was wondering if anyone had recommendations for a textbook that explains...
  30. P

    Lost significant figures through division by exact numbers

    I came across a significant figures problem today that I need information on. The problem is this: "What volume of water can a cylindrical container hold of it is 13.0 cm tall and 12.0 cm in diameter? Show your work and express the answer in scientific notation using significant figures." Of...
  31. X

    Cube root long division method

    On the right paragraph it says "The trial divisor 1200 goes into the dividend 13952, 8 times" Clearly 1200 goes into 13952, 11 times. I don't understand why 8 is (arbitrarily?) chosen. Please help. Thanks.
  32. D

    I Division of a complex number by zero

    Hi I know that division of a real number by zero is not defined. I just came across the following in a textbook on Complex Analysis by Priestley , " we are allowed to divide a complex number by zero as long as the complex number ≠ 0 " Is this correct ? What happens if the complex number is...
  33. matqkks

    I Proof of the Division Algorithm

    In many books on number theory they define the well ordering principle (WOP) as: Every non- empty subset of positive integers has a least element. Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it...
  34. matqkks

    MHB Proof of the Division Algorithm

    In many books on number theory they define the well ordering principle (WOP) as: Every non- empty subset of positive integers has a least element. Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it possible...
  35. SamRoss

    B Trouble with polynomial long division

    I'm reading a book where the author gives the long division solution of ##\frac 1 {1+y^2}## as ##1-y^2+y^4-y^6...##. I'm having trouble duplicating this result and even online calculators such as Symbolab are not helpful. Can anyone explain how to get it?
  36. Mbuso

    Is Zero Divided by Zero Equal to One?

    Why is the division of zero by itself not equal to one,since it is conventional that any number divided by itself is equal to one?,or maybe is zero not a number?
  37. S

    B Euclid Division Lemma: Origins & Legacy

    If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)
  38. jra12222

    Current Division Rule: Solving for Currents

    Hi all, I was working the following example: where I need to find the currents. I tried solving using the traditional V=IR => I=V/R, and then I tried with the current division rule. However with the current division rule the answers don't match. Also according to the answers on the book the...
  39. H

    How Many Electrons Pass Through a Capacitor When Discharged?

    1. A capacitor with a capacity of C= 20μF is connected to a source with a voltage of V=24V. We unplug the source from the capacitor and we then connect it with a wire and the capacitor gets charged in a time of Δt=0.2s. Figure out the number of electrons that pass go to the capacitor and the...
  40. karush

    LaTeX How to Demonstrate Synthetic Division with Latex Efficiently?

    What's the best way to demonstrate Synthetic division with Latex I tried an array but too much open space Mahalo
  41. I

    Different answers for division in Python 3

    Hello Consider the following code in Python3 n = 226553150 m = 1023473145 n*m = 231871064940156750 int(n*m/5) = 46374212988031352 n*m//5 = 46374212988031350 Now since ##n*m## is divisible by ##5##, both should be give the same answer. But the first is wrong and second is correct. What is...
  42. jamiebean

    B Vector multiplication and division

    what is the use of multiplying and dividing a vector by a scalar?
  43. N

    Studying Preparing for upper division courses (transfer)

    Hi, In about two weeks I'm starting my Junior year at a UC, after transferring from a community college. I want to review/get ahead before the quarter officially starts, but I'm at a loss of how to do so. I feel like I may be at a disadvantage to other students because my previous courses...
  44. D

    B Division by Zero: Is it Defined?

    Hi. x2 = x3 / x but x2 is defined for all x and equals zero at x=0 but what happens for x3 / x at x=o ? Is it defined at x=o ? Does it equal zero ? If not what is causing this anomaly ? Thanks
  45. M

    Why must q be the least element for (q+1)a to be greater than b?

    Homework Statement Let a, b be natural numbers then there exists a unique pair (q,r) that are elements of the non-negative integers such that b=aq+r and 0 is less than or equal to r which is less than a I have a question regarding the existence part of the proof, now if I assumed a is less...
  46. Monoxdifly

    MHB Find Polynomial Given Remainder After Division

    11. Given a polynomial with the degree 3. If it is divided by x^2+2x-3, the remainder is 2x + 1. If it is divided by x^2+2x, the remainder is 3x - 2. The polynomial is ... A. \frac23x^3+\frac43x^2+3x-2 B. \frac23x^3+\frac43x^2+3x+2 C. \frac23x^3+\frac43x^2-3x+2 D. x^3+2x^2+3x-2 E. 2x^3+4x^2+3x+2...
  47. opus

    B Intermediate Value Theorem and Synthetic Division

    Say I have a given problem that states: Does the Intermediate Value Theorem guarantee that the following equation has a real solution between ##(\frac{7}{2})## and ##(\frac{9}{2})##? $$3x^4-27x^3+177x^2+1347x+420=0$$ Now what I want to do is determine the sign of x=##(\frac{7}{2})## and...
  48. binbagsss

    LaTeX Long Division in LaTeX: How to Write Each Line

    How do you write each line of long division in LaTeX on here ? Thanks
  49. alijan kk

    How can you simplify complex division with imaginary numbers?

    Homework Statement (1+2i+3i2)/(1-2i+3i2) answer options : a : 1 b: -i c: i d: 0 Homework Equations what is the most easy method to solve it , The Attempt at a Solution are they conjugate to each other ? if they are than z/zconjugate =1 , but how can...