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

    How do I find the other roots of a polynomial if one root is given?

    Here's the problem I have to do: Let f(x)= x^3 -7x^2 +17x-15 One zero of f(x) is K=2-i find all others and write f(x) in a factored form. I ended up getting: f(x)= x^2 -x+2 Is this correct? Thanks
  2. N

    Partial Fraction Question: HELP with Polynomial Long Division

    Homework Statement x^2-x-13/(x^2+7)(x-2) hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions. I also know the answer is 2x+3/x^2+7 - 1/x-2...
  3. D

    How to Integrate Termwise Between 0 and x?

    Not sure when this problem in my book says to calculate by long division the series 1/(1+x) = 1 - x + x^2 - x^3 + ..., and then integrating termwise between 0 and x. I am really rusty on these types of problems and need help understanding how to even begin T.T. Thanks for the help.
  4. S

    MHB Exploring Cosets of a Ring with Division Algorithm

    I'm trying to list the cosets of the following ring and describe the relations that hold between these cosets. R=Z_4[x]/((x^2+1)*Z_4[x]) I'm using the division algorithm since x^2+1 is monic in the ring Z_4[x].Now for every f that belongs to Z_4[x] by the division algorithm...
  5. T

    MHB Long Division with Variables

    I am trying to solve the following problem: $$(\sqrt{x} + \delta)/x$$ Using long division, I get: $$\sqrt{x}$$ On top and I end up with $$-\delta\sqrt{x}$$ On the bottom and am unsure how to proceed from there? I'm sorry I can't write out all my work out as I'm not sure how I could...
  6. MathWarrior

    Lower Division Linear Algebra Vs Upper Divison?

    What is the difference between lower division linear algebra and upper division linear algebra?
  7. C

    Weirdness of polynomial long division algorithm

    "Weirdness" of polynomial long division algorithm Hello. So, i just started to learn about the polynomial long division. As an introductory example, the book presents the long division of natural numbers, claiming that its basically the same thing. The example: 8096:23 Solution...
  8. T

    Studying Recommended upper division classical physics books for self-learning

    Hey guys, I'm an electrical engineering student with a strong interest in physics. I would like to work through classical mechanics, E&M, and thermodynamics books. I'm not sure if there's another subject that is usually covered in classical physics (perhaps waves/optics?) but if so, I'd like...
  9. M

    Sample mean variance and division by (n-1)

    Hi. i wonder how come one doesn't divide with (n-1) when finding the sample mean variance. Homework Equations Shouldn't I divide with n -1 since it is samples i am dealing with? The Attempt at a Solution I don't really have any idea as to why the book uses n. I have googled but...
  10. S

    Long Division to Integrate

    Homework Statement The problem is about solving the homogenous differential equation (x2 + y2)dx + (x2 - xy)dy = 0 using substitution, in this case y=ux. This is the example they go through in the textbook (A First Course in Differentia Equations with Modeling Applications, 9th Edition, Zill...
  11. S

    Probability of Baseball Division Title

    Homework Statement On the morning of September 30, 1982 the won lost records of the three leading baseball teams in the Western Division of the National league were: Braves Won: 87 Lost:72 Giants Won: 86 Lost: 73 Dodgers Won: 86 Lost: 73 Each team had 3 games...
  12. L

    Long Division of cubic polynomial

    Homework Statement \frac{x^3+x^2-5x+3}{x^3-3x+2} Homework Equations The Attempt at a Solution well I'm drawing that long division house with x^3-3x+2 on the outside and x^3+x^2-5x+3 on the inside. I'm seeing that x^3 goes into x^3 one time, so i put a 1 on top of the...
  13. T

    Proof of Altered Division Algorithm

    Homework Statement Show that, for positive integers a and b, there exists unique integers q and r such that a = bq + r and -b/2 < r \leq b/2. Homework Equations We can assume the standard division algorithm holds. That is, for integers a and b, there exists unique integers q and r such...
  14. S

    Modulo division with negative power ?

    if f(x)modg(x) is valid(means , if it yield a remainder) then , can there be negative powers of x in f(x)? for example is (x-29)mod(x2 - 3) possible ? can we do modulo division like this or is it strictly defined only for positive powers of x?
  15. S

    Simple Division Proof: 15|n iff 5|n and 3|n

    Homework Statement Prove that for every integer n, 15|n iff 5|n and 3|n. I have proven the "if" direction. My question regards the "only if" portion of the proof. So far I have: (<--) Suppose 5|n and 3|n. Then there are j,k ∈ Z for which n = 5j and n = 3k. *above, Z stands for...
  16. Beer w/Straw

    Why is division by zero undefined?

    This question seems to befall everyone at one point or another. So much so I begin to get deliberately silly when it is asked http://www.wolframalpha.com/input/?i=Abs%5B1%2F0%5D Anyway, I'm wondering if there is a sticky present on these forums that addresses it specifically. Something...
  17. X

    Abstract Algebra Problem using the division algorithm

    Homework Statement Apply the division algorithm for polynomials to find the quotient and remainder when (x^4)-(2x^3)+(x^2)-x+1 is divided by (2x^2)+x+1 in Z7. Homework Equations The Attempt at a Solution I worked the problem and got that the quotient was (4x^2)-3x-1 and the...
  18. C

    Properties of Logarithms, Division and Multiplication

    Homework Statement Express in terms of logarithms x, y, z or w. Problem: loga(x8w/y2z4) Homework Equations log(u/w) = log u - log w log(uw) = log u + log w The Attempt at a Solution Here are my attempts: As you can see, the answers are pretty similar. I'm assuming...
  19. S

    Courses Difficulty of lower division courses vs. upper division (undergraduate)

    Within the next year, I'm transferring from the local community college to the state university to complete my BS in chemical engineering. Right now I have about 3.5 gpa in my lower division courses (math, chem, physics, intro engineering, etc). Obviously, I'm going to work as hard as I can to...
  20. K

    Division of quarks to leptons result in quark-lepton complementary?

    Hi, I was told by a physics tutor that if you do the following you will result in pi with a complementary between the heaviest quarks and leptons in forms of spin 0 and 1. So I copied what she was saying: ((Top Quark mass/Tau mass)/(Charm Quark mass/Muon mass)) / ((Charm Quark mass/Muon...
  21. P

    Bandwith of frequency division multiplexing (FDM bandwith)

    Hello there! I have a problem with conteptual understanding of the bandwith od channels that use frequency division multiplexing. How i understand that FDM works: We have a transmitter that transmits on one frequency f and the receiver that listens on that frequency. They can communicate...
  22. E

    Every finite domain is a division ring

    I am taking a first course in algebra and I am having issues with a detail in this proof that every finite domain is a division ring. The argument that I used is that (because of cancellation in domains) left & right multiplication by a nonzero element r in a domain R gives a bijection from R...
  23. L

    Did I Divide This Polynomial Correctly?

    As part of solving a DE I need to make this friendlier to integrate: \frac{2u}{1+u^{-2}} I figured trying to divide it couldn't hurt. I got: u^{-1}+u^{-3} I can't type out all the steps easily, I'm on a mobile device at the moment. That answer looks suspect, did I do it correctly?
  24. P

    Proving the Division Property of Prime Numbers in Positive Integers

    Homework Statement (2) P is a prime number and a and b are positive integers . We Know... p | a^6 \ and p | a^3 + b^7. how do i find out how to prove that p | b? Homework Equations if a | b, then a | bx for every x in Z if a | b, and a | c, then a | bx + cy for any...
  25. P

    Proving the Divisibility of 8 and Odd Squares

    Prime Division HELP! Homework Statement I need to be able to understand and likely prove that for any positive odd integer n, 8 | (n^2 -1 ) Homework Equations The Attempt at a Solution odd can be said to be n = 2k +1 so 8 | (2k + 1)^2 -1
  26. F

    Unraveling the Mystery of the '2' in Algebraic Division

    Hello, I can't understand where the '2' came from in this equation. 5x^2y / 10xy^3 = x/2y^2 I can see how the other values were calculated but the '2' before the y^2 is puzzling me. Thanks for any clarification.
  27. I

    Breaking Down Division when divisor is <1

    I haven't been able to figure this out but I am sure it's very simple but I can't understand how to do it. If you take 5 x 0.5, that is the same as 0.5 + 0.5 +... Alright so how do you break a division problem down? I realize how dividing by a number greater than 1 works, but under 1 I...
  28. S

    Why is vector division considered undefined in F=ma?

    Hi, I have seen a discussion similar to the question I am asking right now on the forum before, but I did not understand it and do not know if a conclusion was reached. In F = ma, F, or force net, is a vector and acceleration is a vector. When solving for m, or m = F/a, you are dividing...
  29. P

    Divisibility of (n^2)! by (n!)^n+1: Proven Through Induction

    show (n^2)! is divisible by (n!)^n+1 base case 1 divides 1 so I did the induction and got (n^2+2n)!=((n+1)^n * (n!) *(n!)^n+1 (n^2+2n)*...*(n^2)!=((n+1)^n * (n!) *(n!)^n+1 can we conclude that (n^2)! is divisible by (n!)^n+1 for all n from there because we have the bold...
  30. I

    How Does Matlab Handle Different Types of Vector Division?

    Homework Statement Just tried something out and was wondering. If I have a vector X and do the division 1./X then that will result in a vector in which each element is the reciprocal of the corresponding element in X right? But what does 1/X do? I'm wondering because I noticed that the result...
  31. P

    How do I simplify a binomial division?

    Homework Statement (v-4)/(5v+1) The Attempt at a Solution I'm an engineering student, and I'm taking Differential Equations, but I can't remember how to do simple things like this. A walk through explanation would be very much appreciated, I don't have a lot of time to spare. The...
  32. W

    Inequalities involving division of two absolute values

    Homework Statement How to solve x for these inequality? Homework Equations |x-2|/|x+3|> (x+2) / (x+1) The Attempt at a Solution (x - 2)/(x + 3) > (x + 2) / ( x+1) the left side holds the condition that is x >= 2 however, I wonder the next step. should I crossly multiply so...
  33. F

    Q is closed under division or not?

    Homework Statement Q = rational numbers My professor proved that it is closed under addition yesterday. I kinda understood a bit... How the heck does it work for when n_1 or n_2 = 0?
  34. DocZaius

    Unphysical Division By Zero for Zero Field Location

    Unphysical Division By Zero for Trivial Case of Zero Field Location Homework Statement Q1 and Q2 are two positive charges a distance s apart. Find the distance x from Q1 where the field is zero. Homework Equations E=\frac{kq}{r^2} The Attempt at a Solution Let's put Q1 at the...
  35. T

    How do the steps of successive division get converted into binary numbers?

    So, I can see that it works by dividing a number by its base, recording the remainder, and then repeating until the answer is 0 (instead of a fraction, you wind up with an answer of 0 with a remainder). But how do I convert all the steps' answers&remainders into a binary number?
  36. B

    Proof of the The Division Algorithm

    This is going to be kind of a long post, and I'm citing the author because it's directly from a textbook, but I'm assuming this proof is standard and I won't be doing anything unethical. I'm basically going to post it with my questions interrupting the text. I'm not sure how he got from some...
  37. M

    Solve Binary Long Division: 1010/1001

    Homework Statement I'm trying to divide 1010 by 1001 Homework Equations The Attempt at a Solution So far all I have is _1___________ 1001 |1010.000000000 1001 ------ 0001 I know that 1001 divides into 0001 0 times, but I don't know...
  38. G

    Grade 12 Calculus Problem - Differentiation and Division

    Homework Statement Let p be a polynomial function with p(a)= 0 =p'(a) for some real a. Which of the following must be true? A) p(x) is divisible by x+a B) p(x) is divisible by x^2+a^2 C) p(x) is divisible by x^2-a^2 D) p(x) is divisible by x^2+2ax+a^2 E) p(x) is divisible by x^2-2ax+a^2...
  39. J

    Multiplication and Division of Decimals

    What is division? 12 ones split up into 3 things is 4 ones (per thing.) 1 one split up into 100 things is 1/100 ones (per 1 thing.) Thus, "5 ones split up into 1/100 things is 500 ones (per 1 thing)" is probably better understood as "5 ones split up among hundredths of a thing is 500 hundredths...
  40. P

    Question about the remainder of a division

    I was self-studying Discrete Mathematics and I found the following problem. Homework Statement Show that whenever a and b are positive integers, then (2^a-1)\mod(2^b-1)=2^{a\mod b}-1 The attempt at a solution I don't know if there is a more rigorous way of solving it, but I came up with the...
  41. F

    Synthetic and Long Division for (9x^4 - x^2 - 6x + 2) / (3x - 1)

    Homework Statement I apologise that this is not in LaTeX, but i just couldn't find the codes Use long division or synthetic division: (9x^4 -x^2 - 6x+2) / (3x-1) The Attempt at a Solution So the root is x = 1/3 P(1/3) = 0, no remaindar 1/3 | 9 0 -1 -6 2 ...|...3 -1 0 -2 ___________...
  42. N

    Albinism Allele Copies in Human Cell Division: Meiosis Explanation

    Homework Statement Albinism in humans is controlled by a recessive allele. How many copies of this allele will be found at one of the poles of a cell at telophase I of meiosis in an albino person. A.23 B.4 C.2 D.1 Homework Equations The Attempt at a Solution Let rr be the recessive...
  43. E

    What Is the Real Part of x Divided by the Factorial of -1?

    given (-1)! = \tilde{\infty} , which is complex infinity the real part of \tilde{\infty} is \overline{?} which is "a quantity whose magnitude cannot be determined" as stated in wolfram's site at http://functions.wolfram.com/Constants/ComplexInfinity/introductions/Symbols/ShowAll.html"...
  44. B

    Division of integer square by 4 leaves remainder 0 or 1

    Hi, I am looking for an explanation, if any, on why every integer square leaves remainder 0 or 1 on division by 4. Appreciate your time and help bluemoon2188
  45. S

    Courses How hard are upper division physics courses compared to freshman physics?

    I just took a first semester of a first year physics course for scientists and engineers. Even though I thought that course work was rather rigorous, I did well and got an A in the course. I'm thinking about going into biophysics, but need to have a GPA in the range of 4.0-3.9 since I plan to...
  46. S

    Courses How hard are upper division courses compared to calculus?

    I'm taking calculus for scientists and engineers and was wondering how much harder are upper division courses like partial differential equations, ordinary differential equations, and complex analysis than calculus?
  47. S

    Polynomial Division Homework: Q[x], Z5[x], R[x]

    Homework Statement Divide 2x5+x-1 by 3x2+1 in Q[x], Z5[x], and R[x] The Attempt at a Solution I believe the answer should be the same in Q[x] and R[x] and after division I got 2/3x3-2/9x with remainder 1 2/9x-1. I had trouble in Z5 and would like someone to help me. So far I...
  48. X

    Polynomial Division: Sum of Remainders for 53 < k < 115

    Homework Statement This question was on a test in a math contest I was recently in, and I cannot seem to figure out how to get the answer: Let f(x)=x7+x6+x5+x4+x3+x2+x+1. If k is a positive integer such that 53 < k < 115, find the sum of all distinct k such that the numerical remainder...
  49. S

    What is the Remainder of Polynomial Division in Z5[x] by x+3?

    Homework Statement Find the remainder of x^4 + 3x +2 after division by x+3 in Z5[x] Homework Equations my quotient after dividing was: x^3 + 2X^2 + 4x +1 The Attempt at a Solution I found the remainder to be 4. If anyone has time, I believe I made a mistake somewhere and would...
  50. M

    Number Theory: Division with remainder of factorials

    I'm struggling with how to even begin with this problem. Find the remainder of the division of 75!*130! by 211. 211 is prime, so I know the remainder is not 0. I'm not sure where to start though. Thanks!
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