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

    Modulo Arithmetic: Division Defined?

    Hey, umm... I can't find an answer for this anywhere. if we have a group \mathbb{Z}/p\mathbb{Z} (for sufficient p) under multiplication modulo p, is divsion defined \frac{a}{b} = ab^{-1} ie in \mathbb{Z}/5\mathbb{Z} = \{1,2,3,4\}; would \frac{3}{2} be (3)(2^{-1}) \equiv (3)(3) \equiv 4...
  2. O

    How do I do long division again?

    I forgot long division! :yuck: I just realized something very scary! I totally forgot how to do long division! I can't believe it can some one please explain!
  3. M

    Assembly Divisions: Algorithms & #s Not Fitting Registers

    First of all i'de like to know if there is an efficiant algorithm which assembly uses to divide two numbers. Second I'de like to know how do you divide numbers which don't fit into a register. I'm talking about an array of bytes in RAM to be divided. 10x!
  4. M

    Fast Algorithm for Division w/ Remainder - Division Revision

    Guys I need a fast algorithm to perform division with a remainder. It has to be very fast though...
  5. R

    Could someone explain why is division distributive over addition ?

    could someone explain why is division distributive over addition ? It's not intuitive to me. Thanks Roger
  6. R

    (2x^2 - 3x+6 ) / (2x+2) division

    I don't understand how this works : (2x^2 - 3x+6 ) / (2x+2) I don't really understand the case using numbers either but we never divide by a+b+c etc , (ie we just divide by a single number rather than 3+5 for example) Please explain step by step how it works. Also, why isn't the...
  7. S

    Cell division and chromosome errors

    What changes would have to be made to a cell so that when it divides the genes in the daughter cells are exactly the same,in the same order and number on the chromosomes, as they were in the parent cell?
  8. RadiationX

    Integrating e^x/(e^{2x} + 1): Long Division?

    i'm having trouble rewriting this integral:\int\frac{e^x}{e^{2x} + 1} so that it will be in the arctan formula: should i use long divison here? if it were not for the e^x in the numerator i'd be fine.
  9. E

    Divide By Zero: Is It Ever Logical Not To?

    Can somebody please tell me any case where it is logical to NOT divide by zero? I know division by zero is illogical itself, but usually when you divide by zero the result should be zero anyway. :rolleyes:
  10. S

    Solving the Equation: k^3-3K2+31k-37=0 with Synthetic Division

    solve the following promblem Y^(,,,)-3y^(,,)+31y^(,)-37y=0 i let y = e^kx y'= ke^kx y''=k^2e^kx y'''=k^3e^kx so i got this k^3e^kx-3(k^2e^kx)+31(ke^kx)-37(e^kx)=0 e^kx(k^3-3K2+31k-37)=0 so, (k^3-3K2+31k-37)=0 now i have to find (K) how should i solve for...
  11. L

    Solve Polynomial Division with Synthetic Division | Step-by-Step Guide

    I was wondering if you could help me out with this problem. Please explain how to solve using synthetic division. I need to know how to solve it. \frac{6x^4-3x^3+5x^2+2x-6}{3x^2-2} The answer is 2x^2-x+3
  12. S

    Proving the Division of Power Series: A Rigorous Approach

    I'm trying to show that the quotient of two power series Sum(n=o, infinity)[an*z^n] and Sum(n=0, infinity)[bn*z^n] is the power series Sum(n=0, infinity)[cn*z^n] where c0=a0/b0 and b0cn= (an-Sum(k=0, infinity)[bk*c(n-k)]). Is there a way of showing this by (Sum[bn*z^n])(Sum[cn*z^n])=Sum[an*z^n]...
  13. M

    Solving a Polynomial Division Problem: Remainder = 5 & 7

    Given that a polymial p(x) is p(x)= (x-1)(x-2) q(x) + 2x+3 where q(x) is also a polynomial Find the remainder when p(x) is divided by (x-1)(x+2) where the remainder divided by (x-1) and (x+2) is both 5 and 7 respectively. I don't know even where to start ! so please help, thanks alot.
  14. B

    Proof of ab=0 <--> (a=0 or b=0) without Division

    Is there a proof of a*b=0 <--> (a=0 or b=0) that does NOT involve division? Also, my discrete math professor has claimed that mathematicians tend to avoid the concept of division. How accurate is this claim for discrete mathematicians? What is the reason for it?
  15. M

    Master Long Division: Get Help After 5 Years of Not Using It

    It's been at least 5 years since I've used long division. I managed to do the first half but I have no clue on how to finish it. I will appreciate any kind of help. -------
  16. J

    Algebraic Division: Solving Step by Step

    I didn't really know where to put this, but I thought I'd post it in General Math. Any way, here's the problem, I'd like it solved step by step, please. a4 (a to the fourth power) + Oa3 (a to the third power) + 9a2 (a squared) + Oa divided by: a2 (a squared) - 3a + 9 Thanks in...
  17. A

    Solve Polynomial Division: -6x^4+2x^2-8x+1 / 2x^2-3

    I have been trying two problems for the longest time, and no one is able to help me I am so stuck, I know how to divide polynomials using long division and synthetic division using simpler numbers but I just can't do these two questions and my course is online, so I can't even ask my teacher...
  18. D

    LaTeX Typesetting Long Division in LaTeX: Tips and Tricks for Accurate Equations

    Does anyone know a way to typeset a long division in LaTeX? I'm particularly interested in: \frac{1}{\cos x} = \frac{1}{1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots} Thanks
  19. M

    Division theoryand Prime Number theory

    Hey, A while ago i hear about finding the division number theory [Tell how a number can be divied be another unmber as a general formula]. And i am wondering if there is a theory "desicovered" the pattern of the prime numbers. Or at least a fixed pattern for predicting some of the prime numbers...
  20. R

    Solving Division: Understanding Zero as a Placeholder

    HI please can someone help me with this quick question on division : If I have to do 3 divided by 4 ____ 4 |3 4 doesn't go into 3 so I put a zero on top . When it gets to 4 into 2(from 30-4x7), it doesn't go, so why don't I put a zero on top but instead put a zero beside the...
  21. N

    Vector Division: Is It Possible?

    From school, we've had addition, "subtraction" of vectors and then scalar multiplication, dot & cross products. I have never come across dividing a vector by another. Is there such an operation? Eagerly awaiting enlightening replies, Nanveeth
  22. N

    Cell Division: An Overview for Beginners

    could anybody be kind to explain what is cell division to me please? i only know is that its chromotins duplicated.
  23. N

    Triangle Area Based on Segment Division

    Hi all, I'm working on this problem in my Geometry class, and am having a bit of trouble coming to a conclusion. The problem as given is (I've attached the figure to this thread): From this information, I have deduced that triangle DCB is right isosceles, with DC = CB. Also, since <DBC...
  24. B

    Is the Current Science or Trash Division Helpful?

    For a long time now I have pondered over our universal acceptance of empirical science, our methods, our successes...and its drawbacks. At the same time, I see a whole lot of unanswered questions, some of them "factual", but because they cannot be the subject of grant or that it requires a...
  25. Shahil

    Division by Zero - Can it be Done?

    Division by ZERO! Hey guys! Was just pondering... ALL my mathematical subject lecturers go on and on and on about trying to avoid division by zero. Fine - after all, it makes logical nonsense to divide by zero but my pondering thoughts led me somewhere... Is it possible to do some...
  26. S

    Quotient rule for derivatives (algebraic division help?)

    Hi, I'm currently reading "Calculus Made Easy" and ran into a road block. I'm reading this in my spare time so it's not school work or anything (I know some forums have policies about this is why I mention). The answer is there. I just want to know how to go about doing this problem. It...
  27. S

    Problem with polynomial division and 'i'

    I was learning polynomial division, and I can do most problems, except this one which is bothering me. : 3x^2 + 2x + 7 --------------- (1+i)x - 2 How would I divide something like that? Nothing is working. Thanks.
  28. Shahil

    Heaviside Method Division By Zero

    Help! :confused: Here I am busy doing some Laplace Transforms for my Maths 2 paper on Monday when suddenly to my surprise, an apparent "mistake" appears! GASP! :eek: It's got to do with the Heaviside "cover up" method. To work out a problem, you need to multiply the opposing side by...
  29. C

    Cell Division of Blood Cells: Facts and Q&A

    Hi all, Before I ask a Q about blood cancers, can I just check - is it right that cell division of blood cells takes place only in the bone marrow (and not in the bloodstream or anywhere else)? Thanx Charles
  30. C

    Division Algorithm: Find q & r for a=-5286 and b=19

    If I have to find the quotient q and the remainder r and: a = -5286 b = 19 How do I go about writing down the steps for this algorithm? I know what the answer will be, but I need to be able to use the division algorithm to prove my answer. Like I know if: b > 0 and a < 0 (which in this...
  31. R

    Exploring Cancer: Genetics, Cell Division & Treatment

    Just seen an interesting documentary about the breakthrough in Cancer treatments. The programme gives a brief discription on cell division and how doctors think the way forward for treatment is changing due to the Understanding of Genetic (genome) discovery. Anyway I was fascinated by the film...
  32. abstract

    Starting from 2 to remove division by zero from the equation.

    The number 2 What if the number 2 is the origin of whole numbers? (Instead of 0) The criteria for a whole number would contain that a whole number would primarily need to be wholly divisble by 2. does 2/2 = 2 as there are 2 combinations of the halves of 2 I think this can be...
  33. P

    Multiplication and division in physics

    What does it mean to multiply two physical quantities? Ie: For electrical potential energy the equation is Ee=kq1q2/r Where k=Coulombs constant, q1 and q2 are charges in Couloumbs and r is the distance between the charges What does it mean to multiply q1 and q2?
  34. Monique

    How Does Plant Cell Division Differ from Animal Cell Division?

    I am wondering about the differences between plant vs animal cell division, mainly about cytokinesis. Is the following a true generalization? Plant daughter cells separate by forming membrane vesicles that line up in the center of the cell and fuse to form new plasma membranes. Animal...
  35. A

    How can we define division without using addition?

    Multiplication is defined as repeated addition. 3x5 = 5+5+5 How do we define 10/2?
  36. A

    How is division defined in mathematics?

    Multiplication is defined as repeated addition. 3x5 = 5+5+5 How do we define 10/2?
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