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. M

    Division of Vector: Learn How to Perform A/B Expression

    How can vector division be performed? Tell me the procedure how I would perform following expression: If A= 4i + 5j + 6k and B= 1i + 2j + 3k what will be A/B?
  2. X

    Does d dividing n imply phi(d) divides phi(n)?

    Prove that if d divides n then phi(d) divides phi(n). Thanks
  3. T

    Integration by long division problem

    Homework Statement Consider the indefinite integral of (4 x^3+4 x^2-96 x -100)/(x^2-25)dx Then the integrand decomposes into the form ax + b + c/(x - 5) + d/(x + 5) Find a, b, c, and d. Then find the integral of the function. The Attempt at a Solution Using long division...
  4. S

    Cell Division Mysteries Unraveled: Answers to Your Top Questions

    I had some questions... 1. How come garlic extract increases the hayflick limit? http://www.smartskincare.com/aging/aging-mechanisms_cellular-clock.html 2. How come feeding the cell more results in its growth in size?(if that's so then why don't liver cells grow?) 3. I have read...
  5. P

    Polynom Division: Finding the Reminder with (x-a)(x-b)

    Homework Statement When we divide the polynom P(x) with x-a, we receive reminder \alpha, and if we divide P(x) with x-a, we receive reminder \beta. What will be the reminder, if we divide P(x) with (x-a)(x-b)? Homework Equations The Attempt at a Solution P(x)=(x-a)f(x) + \alpha...
  6. D

    Find Factors of Polynomial Division: x-2 in Q[x] & x+1 in Z5[x]

    1. Polynomial division a) For what values of k is x-2 a factor x^4 – 5x^3 + 3x + k in Q[x]? b) For what values of k is x+1 a factor of x^4 + 2x^3 – 3x^2 + kx + 1 in Z5[x]
  7. D

    Simple Algebra Division question

    Hello, I am not grasping how to deal with multiple divisions properly. If I have a/1 divided by b/1 divided by c/1 How do I know if the compressed form is ac/b or a/bc?
  8. S

    Meiosis I Cell Division: Understanding Allele Distribution in Daughter Cells"

    Homework Statement If we follow meiosis in a diploid heterozygote, the two alleles are, following the first cell division, a. no longer together in one cell b. together on a chromatid c. present only as mutants d. blended into a new mix e. chromatids...
  9. C

    Run through the steps of this division

    Homework Statement Please could someone run through the steps of this division ((2(x-1)^2) e^-x)/(1-x) Homework Equations The Attempt at a Solution is it necessary to multiply out this bracket?...im quite confused. thanks for help
  10. B

    Proving division of continuous functions

    Homework Statement Okay, so if f and g are continuous functions at a, then prove that f/g is continuous at a if and only if g(a) # 0 Homework Equations Assuming to start off the g(a)#0, by the delta-epsilon definition of continuity, basically, We know that |f(x)| and |g(x)| are bounded...
  11. A

    Basic: Misunderstanding of some division concepts

    Hey, I see a lot of things going on with some mathematical equations that even I would do, but I'm always confused by them for some reason, such as: \frac{\sigma-\delta}{\sigma} Wouldnt this just be equal to: \frac{\sigma}{\sigma} - \frac{\delta}{\sigma} = 1 - \frac{\delta}{\sigma} I...
  12. T

    Seeks Solution to L-Shaped Land Division Puzzle

    Homework Statement Here is the exact wording of my sons problem When a certain land owner died this l shaped plot of land was left to be shared among four children the only stipulation of the will was that the land must be divided into four congruent plots. show how this can be done. The...
  13. E

    Solving Vector Division: Breaking Down the "12 Left" Answer

    The question is: Vector b/a=_____ I guessed a few times (losing a point each time it was wrong) and finally got the answer. The answer is: 12 left The site (it's online homework) then gave this explanation: "To the driver of the Audi, the Buick appears to be moving to the left and...
  14. arivero

    3,4,6,10: division algebras, the brane scan &c

    Baez refers to the Brane Scan in a old TWF, #118. You can also find a more recent depiction in http://arxiv.org/abs/hep-th/0301037 Duff also refers to original work from German Sierra (http://www.slac.stanford.edu/spires/find/hep/www?j=CQGRD,4,227 ) and from J.M. Evans...
  15. S

    Synthetic division or Long division of polynomials?

    How do i know under which circumstances to use synthetic and when to just do regular polynomial division? do they not both give the same results?
  16. U

    Is There a Trick to Check if a Number is Divisible by 3?

    Okay, this may be a silly subject for a thread, but do you know that trick where you check whether a number is divisible by 3? The one where you add all the digits of that number, then add all the digits of the number you get as a result and so on, until you're left with a single-digit result...
  17. L

    Programs GPA of Upper Division & Lower Division courses and M.S degree

    I just graduated from a University. I was in Mechanical Engineering major. My overall GPA is 3.5. However, I have some problems with my Lower-level division courses. While I was in Freshman and Sophomore years, I had some Ds, Fs and W in some Math and G.E subjects. I did very very well in...
  18. B

    ASM Newbie Question: 10/6 Byte Division

    Hi, I am new here and I got a newbie ASM Question: How to divide, say, a 10 by 6 bytes number if the DIV (or IDIV) opcode only supports a 8 by 4 Bytes division? Thanks in advance
  19. O

    Convince a classmate that division is not associative.

    Homework Statement How would you convince a classmate that division is not associative? By "associative" the book aims at the Associative properties of multiplication and addition. Is this equation correct? a/(b/c) = (a/b)/c Homework Equations a + (b + c) = (a + b) + c a(bc) = a(bc)...
  20. K

    I am looking to find some lecture notes on upper division linear algebra

    can anyone help me?
  21. RadiationX

    Question: How do I prove the current division law for two resistors in parallel?

    My professor gave us the task of proving the current division law for two resistors in parallel. I know that the voltage across parallel resistors is the same, and that the sum of the branch currents adds to the sum of the total current. Here is the question: Prove that I_1=...
  22. P

    Find the remainder of a division

    Hi all! Could anyone help telling me the way to find the remainder of the following divisions: 1. (x^2006+x^1996+x^1981+x+1):(x^2-1) 2. (x2+x3+x5+1) : [(x-1)(x-2)] Thanks
  23. E

    How do I apply the chain rule in division rule for this calculus problem?

    Homework Statement y = (2x-3)/(x^2+4)^2 Homework Equations The Attempt at a Solution I am trying to relearn the calculus that I forgot from many moons ago. I am struggling with the chain rule in the above example. I tried to set it up as follows: This is what I know...
  24. S

    How can I solve this advanced polynomial division problem?

    Some of you may have read my troubles that I had in this thread https://www.physicsforums.com/showthread.php?t=162079 Now I am having more troubles with more advanced problems. I started with this problem: [4y^2 - 7y - 12] / [(y)(y+2)(y-3)] The problem is that I set it up the same...
  25. S

    Polynomial Division: Solving Denominator > Numerator

    I just can't remember how to do this! I've been to several sites suggesting synthetic division and other guides on polynomial division but i can't get it into my head and its driving me wild. (8x-8)/(x^2+3x+2) synthetic division doesn't work here because the denominator is larger than the...
  26. M

    Complex Division: Solving Proof for Dividing 2 Complex Numbers

    I'm working on the proof that two complex numbers can be divided from Alhford and I'm completely s(t)uck. I've gotten as far as: a = gx - dy b = dx +gy from (a+ib) / (g + id) where a+ib = (g + id)(x+iy) I've managed to get x={\frac {b-{\it gy}}{d}} and done the same...
  27. A

    Division by Zero: What Does it Mean?

    Good morning all I want to know why 0 divide anything = zero, and why division by zero is undefined? regards Blog Insight: Division by zero
  28. K

    Solve Weedy Willie's Division Puzzle

    A couple of years back, I came across a nice problem in a puzzle magazine. PROBLEM: Weedy Willie was getting too old to work the land alone so he decided to divide his cornfield between himself and his four sons in proportion to their five work rates. He knew that Rastus, Wig, Twig and Swig...
  29. mattmns

    Proving the Evenness of Fibonacci Numbers through Division by 3

    Here is the question: ------ Prove that f_{n} is even if and only if n is divisible by 3. (f_{n} is of course the nth Fibonacci number) ------ Proving that n is divisible by 3 => f_{n} is even is easily done by induction, but the other implication is eluding me. It is easy to show that f_{n}...
  30. M

    Is Trial Division Primality Check Considered in Polynomial Time?

    Greetings, This is very simple, and obviously I'm missing something trivial, but I still don't get it. An algorithm is said to run in polynomial time if it runs in O(n^K) time. That's why dijkstra for example, who runs in O(V^2), runs in polynomial time. That said, my doubt is...
  31. B

    Division with polynomials involving the remainder theorem

    Two questions, first, I solved something, but I was just playing around with the numbers, and I didn't really know what I was doing, nor did I really understand it after I was done. The question is as follows: When x + 2 is divided into f(x), the remainder is 3. Determine the remainder when x...
  32. mattmns

    Division Theorem [proof by induction]

    First let me say that this is not technically the Division Theorem that I will be proving. Our book calls it the Euclidean Algorithm, but this is clearly not true, it is closer to the Division Theorem, imo. Anyway, my book wants us to prove the following proposition. Note: Here natural...
  33. I

    Size of the division of a segment in infinite intervals

    Dear people of this forum, Assume we have an interval of a line [ a, b]. Now, let us divide this interval in many ( infinite ) subintervals of finite size. ? What will be the size of these many intervals, equal or unequal, when the number of subintervals tends to infinite?. ¿there is any...
  34. W

    Division with variables (I think I'd call this double division)

    I don't even know where to start with this question, someone help please. I don't know how to LaTeX this question so please bare with me: ( ( x / y ) - ( 4y / x ) ) / (x + 2y) It's two fractions over a binomial. Hope this isn't to unclear :(
  35. N

    Long Division Puzzle: Solving for Unknown Values Using Long Division Method

    I found in this book the other day the following puzzle (but the book did not give any answer), if someone can do this could you explain, step by step proceedings please as I just get no where. The question is this: We are given the following division (each x is an unknown value) xx /...
  36. G

    Frequency division multiplexing

    Apparently a standard FDM scheme for telephone signals is to multiplex 12 voice channels, each occupying 4kHz bandwidth, into a group signal with 48kHz in the range 60-108kHz, using subcarrier frequencies from 64-108kHz in 4kHz increments, and using only the lower sideband of each modulated...
  37. Curious3141

    Polynomial long division by Ruffini's synthetic method

    http://en.wikipedia.org/wiki/Synthetic_division A faster method for linear divisors than traditional long division, it has served me well through school and beyond.
  38. G

    Screw Gauge Pitch: Length of Main Scale Division?

    In a screw gauge, the pitch is defined as the distance traveled in one rotation. Is it also equal to the length of one main scale division? If the length of one main scale division is not given, then can we take it to be equal to the pitch? Or do we take it as equal to some other default value.
  39. B

    Division of Characteristic Functions

    I'm in graduate analysis this year, but I've been out of school as a teacher for 6 years so I'm a bit rusty. Any help would be appreciated on this simple question. My apologies for not knowing the Math-type. Yesterday in class we were discussing an example which demonstrated the...
  40. S

    Partial fraction expansion (polynomial division)

    If we're asked to expand an irrational partial fraction, we need to rationalize it first, right? I've forgotten (well not totally) how to perform polynomial division. Here are a few examples: 1. (1000x +1000000)/(.4x + 200). For this one I got 50000. 2. (500x + 60000)/(x+100)...
  41. L

    Time Division Multiplexing

    hey y'all! could someone please explain to me how to devise a commutator configuration when given a number of signals and their bandwidths. Example: with four signals bandlimited to W, W, 2W, 3W. Give a possible sequence for a period.
  42. R

    Polynomial Division puzzler(well to me anyway :P )

    O.K I factored and reduced an equation I am doing down to (s+5t)/(t-s) I could not figure it out so I went to webmath and used a calculator to find out the answer so I could reverse solve the problem. The answer is 1 according to webmath. Any hints on how to get started on this becuase I...
  43. F

    How Does Synthetic Division Work?

    I'm always curious as to how this works? I mean, it's amazing that, even though dividing by binomials, that this sort of mechanism works but I don't understand quite the qwerks behind this. Can someone fulfill my curiousity?
  44. H

    HighSchool Calculus Polynomial Division Help

    I was just doing my homework when I stumbled on this question. I don't understand it and I was wondering if someone could help me through it (don't just do it though, because I want to learn HOW to do it :smile: ) When 8x^3+4x^2-px+6, p E R, is divided by 2x-1, the remainer is 3. Determine...
  45. H

    Polynomial Division Help - x^3 + 4x^2 - 3x - 12 & -x^3 + 75x - 250

    I can't seem to get it... I need some help with 2 of the problems below: x^3 + 4x^2 - 3x - 12 over x^2 - 3 and -x^3 + 75x - 250 over x + 10 I've tried tutorials and everything, I can get a few but these are just a little tricky for me. Any help is appreciated. :)
  46. MathematicalPhysicist

    Division by Seven and Modular Arithmetic: The Ultimate Guide

    is really the only way of checking which number is divisble by 7 is by modular arithematics?
  47. J

    Imaginary Number to Indicate Division by Zero?

    Forgive me if I'm being ignorant, but this recently occurred to me. We all know division by zero is undefinfed, but \sqrt {-1} used to be undefined too, until i was created. Has anyone ever proposed an imaginary number to indicate the result after division by zero?
  48. K

    Why is standard division considered the natural way to partition a number?

    This question probably falls more in the philosophical arena than the practical, but I didn't see any available "math philosophy" forums, so here goes. I've always found it curious why, out of all the possible ways to partition a number, is standard division a/b considered "natural." That is...
  49. B

    Finding Multiplicative Inverse of 23 in Z_31

    There's something that's been bothering me with the division algorithm for a while. a = dq + r where r < |d| and a,d,q,r are integers. This can be used to find the multiplicative inverse of an integer in Z_m where m is an integer if certain conditions are satisfied. For example if I had two...
  50. U

    How do you know if you're smart enough to handle upper division physics?

    how do you know if you're smart enough to handle upper division physics? i think i might want to do biomedical engineering for a career. but I am considering doing physics for undergrad w/ a BME minor. i enjoy physics and believe it would increase my problem solving skills. the only...
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