What is Addition: Definition and 651 Discussions

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.
Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months, and even some members of other animal species. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.

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  1. A

    Mass addition due to gravitational acceleration

    I read an article about super massive black holes that are millions a billion times larger than our sun. In reading this article i began thinking about gravitational acceleration and what the effects would be on incoming objects. I ran through a bunch of equations and found that the mass gain...
  2. T

    Quantum Mechanics - Addition of Angular Momentum

    Just when I think I've understood addition of angular momentum, I find a problem that completely questions everything I think I know. Okay so here's the problem: question 3/II/32D on page 68 http://www.maths.cam.ac.uk/undergrad/pastpapers/2005/Part_2/list_II.pdf . For the possible values of J...
  3. P

    How do I introduce my kid to addition and subtraction?

    How do I introduce my kid to addition and subtraction? Is there any internet tool for me to support?
  4. Hemmer

    Fortran Parallel FORTRAN output varies with addition of arbitrary WRITE statement

    Hi there, I've been puzzling over the following code (which works in serial). It produces radically different answers if the (blank) WRITE(*,*) is included or not. Any help greatly appreciated! eps = 0.0 !$omp parallel do default(none) private(i, j, current_angle, current_energy) &...
  5. G

    Velocity addition expressed as gamma

    if object A is moving with gamma=x in one direction and object B is moving with gamma=y in the opposite direction then what is the gamma factor for object A as it would be calculated by object B? I know the velocity addition rule for relativity but I can't find anything on the net about...
  6. M

    Finding the intersection of subspaces, and addition of subspaces

    Heres the question: Let {u,v,w} be a linearly independent set of vectors of R^4. Let E = span{u,2v} and F=span{w,v}. Find EnF and E + F. i really have no idea other than i guess if 1/2u=w and v=v, then the EnF can be defined by that, but I'm not sure if that is right! :(
  7. N

    Help me Understand Closed Under Addition and Closed Under Multiplication

    Help me Understand "Closed Under Addition" and "Closed Under Multiplication" Linear Algebra...matrices...etc Examples would be great. Thanks.
  8. Y

    Velocity addition ain't what it used to be

    In special relativity, the velocity-addition for colinear velocities u and v is given by (u+v)/(1+uv/c^2), but for non-colinear velocities the formula is more complicated and is not symmetric in u and v. But since the reciprocal velocity of v is -v then the reciprocal of (u+v) should be -(u+v)...
  9. T

    Adding dBm to dB from Rappaport's Wireless Comm.

    How does it become valid to add a dB with dBm? I found in a book that the author did like the following: 60dBm - 155 dB = - 95 dBm Isn't it necessary to convert 155 dB into dBm or vice versa and then doing the algebra? The book is wireless communication by Theodre Rappaport.
  10. N

    Simple hexadecimal addition question

    Homework Statement I have to hex numbers, x1100 and x3301, that I want to add. I tried to convert them to binary and and them, then convert back to hex-wrong. Tried a straight 1100+3301 addition with the answer being hex, and even used my ti-89 to add them, it can do conversions so why not...
  11. J

    Alternative formula for the Rule of Addition not working for some problems

    In probability, the rule of addition is: P( A \cup B) = P(A) + P(B) - P(A \cap B) This can be written as P( A \cup B) = P(A) + P(B) - P(A)P(B) However, I've seen that using both formulas for the same problem gives different answers in some problems. Does anyone know why? Is there a...
  12. X

    Law Of Sines, deducing addition formula

    I'm attempting to self study mathematics. Will be starting college next year and recently got a good score on the SAT Math 2 (~700). I bought "Geometry Revisited" by Coxeter and Greitzer, hoping to gain a bit more knowledge of Geometry. I got stuck on the first question! Until now, all the...
  13. E

    Subspace Proof (using addition and multiplication)

    Homework Statement Determine whether or not W is a subset of R4 W is the set of all vectors in R4 such that x1x2=x3x4 Homework Equations Two methods. u+v (addition) cu (multiplication) The Attempt at a Solution I having trouble getting the hang of subspaces. I thought I was getting close...
  14. Rasalhague

    Nonlinear Addition of Four-Vectors in Relativity: Exploring the Inconsistencies

    Since the "tensors" of relativity are defined with respect to the tangent spaces of a pseudo-Riemannian manifold, which include velocity vectors (i.e. timelike tangent vectors), this might be taken to suggest (carpet-from-under-feet-ingly) that none of the objects called tensors in relativity...
  15. kreil

    Relativistic Velocity Addition

    Homework Statement Show that the addition of velocities implies the following: - If | \vec V | < c in one inertial frame, then | \vec V | < c in any inertial frame - If | \vec V | > c in one inertial frame, then | \vec V | > c in any inertial frameHomework Equations V^{x'}=\frac{V^x...
  16. H

    Deserate me with Vector addition.

    Homework Statement Graphically determine the resultant of the following three vector displacements: (1) 34m, 25 degrees north of east;(2) 48m, 33 degrees east of north; and (3) 22m, 56 degrees west of south. Homework Equations Vr=V1+V2+V3 x=mag x cos of angle y=mag x sin of angle...
  17. J

    Vector Addition: Calculate Magnitude of Sum

    Homework Statement A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be: a. zero b. 3 c. 12 d. 47 e. 50 Homework Equations c ^2 = a^2 + b^2 The Attempt at a Solution I was not entirely sure on what to do. I tried using the...
  18. S

    Can commutativity of multiplication and addition under real numbers be assumed?

    Homework Statement so.. let the operation * be defined as x*y = x + y + xy for every x,y ∈ S, where S = {x ∈ R : x ≠ -1}. Now i have proven associativity, existence of an identity and inverses, all without commutativity, but i must show that this is an abelian group, so now i have to show...
  19. D

    Vector Addition Homework: Mag & Angle of Average Velocity

    Homework Statement A train at a constant 47.0 km/h moves east for 44 min, then in a direction 57.0° east of due north for 27.0 min, and then west for 61.0 min. What are the (a) magnitude (in km/h) and (b) angle (relative to north, with east of north positive and west of north negative) of its...
  20. S

    Optimizing Cable Direction for Minimum Force in Vector Addition of Forces

    Homework Statement Three cables pull on the pipe such that they create a resultant force having magnitude FR. If two of the cables are subjected to known forces, as shown in the figure, determine the direction θ of the third cable so that the magnitude of force F in this cable is a minimum...
  21. S

    Vector Addition of Forces: Finding the Resultant Force

    Homework Statement [PLAIN]http://img138.imageshack.us/img138/918/79095797.png Find AE resultant forceHomework Equations The Attempt at a Solution I don't know where to start, I can find some of angle, but still I don't get it, Also this question is in my test, I remember the question said AB...
  22. H

    Kinematics in 2 Dimensions: Vector addition

    Homework Statement With the diagram and the data answer the question: What is the magnitude of A + B? http://i995.photobucket.com/albums/af79/huybinhs/w.gif DATA: theta1 = 33.7 deg, theta2 = 141.9 deg , A = 3.6cm, B =8.3cm. Homework Equations This is an example of vector...
  23. U

    Simplifying Vector Addition: Confusion with 360 & 270 Degree Forces

    When adding the resultant of two or more forces i get confused when adding forces that are on 360 and 270 degrees. Like the question is 6 Newtons on 360 degrees, i don't get how they get -6, when cos 360 is 1 can anyone help me??
  24. T

    Another standard addition problem

    Homework Statement Palladium(II) forms an intensely colored complex at pH3.5 with arsenazo III at 660 nm. A analyst is trying to analyze the palladium content in a meteorite. First 2.534g of the meteorite was digested in strong mineral acids. The resulting solution was then evaporated into...
  25. M

    Trig' Identities - Addition Formulae

    Homework Statement Given that cos C = 12/13 where C is a reflex and sin D = 3/5 where D is acute, find the exact value of cos ( C + D ). Homework Equations The Attempt at a Solution I used the Addition Formulae: cos(A+B) = cosAcosB-sinAsinB cos(12/13)cos(2/5) -...
  26. T

    Addition of a System of Coplanar Forces

    1. If the problem statement, all variables and given/known data The resultant force acting is directed along the positive x-axis, determine the magnitudes of F2 and the resultant force And that F3x=4 and that F3y=3 (its a right angle 3-4-5 triangle) Homework Equations F1=F1x +F1Y F2=F2x +F2Y...
  27. A

    Addition with a cantilevered balcony

    I am designing an addition with a cantilevered balcony and am wondering if it is physically possible. the deck is 24' long with 12' extended past I will be using W12 x 96 (massive) it will be held up with two rows of columns that are 12' apart. my question is if the foundation of the columns are...
  28. M

    Help with addition NaCl to water

    If you want to extract more polar compunds out of water, you add NaCl to make the water more polar. But why do the really non polar compounds give a less recovery with the salt addition? (For example Prosulfocarb and Tri-allaat) (Pesticides) The extraction occurs in a glass tube, so the...
  29. stevmg

    Exploring the Invariable Speed of Light: Einstein's Velocity Addition Formula

    Using drudkh's example cited above and using Einstein's velocity addition formula, closure speed between a particle moving to the right at v and light coming from the right and moving left at c would still be c. Why? Let's use v as the velocity of the particle expressed as a fraction of c...
  30. N

    I with vector addition and subtraction

    Homework Statement Alright so I have an object being pulled from two sides at an angle like the picture below. I want to figure out a third force that can be added to keep the object in the middle of the two sides. Are the directions of the components I drew correct? (There is an actual...
  31. D

    Help with applications of vector addition

    I can't seem to draw this diagram. A sign weighing 98N is suspended from the middle of a 4m long chain. The ends of the chain are attached to a ceiling at points 3m apart. Okay so i drew a diagram with a horizontal that is 3m and the chain hanging from each side is 2m long and the object is...
  32. B

    Addition of Velocities in Special Relativity

    The problem is in an Algebra book but the jist of it is about calculus/analysis. If G is the interval (-c,c) and the operation is addition of velocities in Special Relativity, (that is: x \circ y = \frac{x+y}{1+\frac{xy}{c^2}}) then decide whether G is a group. At first I thought it wasn't...
  33. F

    Gravitational Model of Tides: Earth and Sun Potential Addition

    I have a question about the gravitational model used to describe tides: Is it correct to simply add the tide potentials respectively due to Earth and sun as most people do? (see for instance a good example of this approach in Eq 9 of: http://arxiv.org/PS_cache/physics/pdf/0701/0701301v1.pdf)...
  34. D

    Pendulum question - Vector addition of forces

    Homework Statement A 1.0 kg pendulum bob is suspended from a string 1.0 m long. The pendulum swings until the string makes an angle of 22° with the vertical. At this point, if the pendulum is held with a string fastened to the bob and held horizontally, what would be the tension in the original...
  35. fluidistic

    Prove: EM Waves Addition Superposition Equivalence

    Homework Statement Show that the superposition of three waves with frequencies \omega _c, \omega _c + \omega _m and \omega _c - \omega _ m and same amplitude are equivalent to another wave of frequency \omega _c which is modulated by a sinusoidal wave with frequency \omega _m, i.e. E=E_0 \left...
  36. J

    Can Matrix Addition Allow for Cancellation?

    Ques.)-If A,B,C are three matrices such that A+B = A+C, then prove that B=C. Can i cancel out the A's in LHS and RHS ?
  37. O

    Boolean algebra- cancellation property of addition

    1. Prove that for all boolean algebras if x+y=x+z and x'+y = x'+z then y=z. 2. Homework Equations : x+x' = 1, xx'=0, basically we are allowed to use the usual boolean algebra properties. 3.Attempt: This the second part of a problem, in the first part we had to give and example of...
  38. T

    Observed speed of light [actually about relativistic velocity addition]

    I apologize if this is a repost, my original post didn't seem to take. If you accelerate a particle to 99% the speed of light and accelerate another particle to 99% the speed of light directly into the path of the first would this not create the observed effect from either particle that the...
  39. I

    Relativistic Addition of Velocities

    Homework Statement Faraway Point starbase launches a probe toward the starships approaching from the same direction. The probe has a velocity relative to the Picard of -0.895c. The Picard approaches starbase Faraway Point with a speed of 0.795c, and the La Forge approaches the starbase with a...
  40. T

    Programming Binary Addition with a Turing Machine

    hello, One can wonder what is the relation between the title of this thread and the subject of quantum mechanics, well, i was reading in a book about quantum computation and information and it was talking about computer science in some chapter where it shows a basic understanding of Turing...
  41. X

    Standard Addition Chemistry problem

    Homework Statement Homework Equations Not completely sure, but I believe equation is: Cx = bCs/mVx cx = concentration of sample b= y-intercept cs= concentration of standard m=slope Vx=volume of sample The Attempt at a Solution I plotted the values on a graph with Absorbance...
  42. D

    Addition of exponents disconnect

    Homework Statement (35.709 + 5.789)(10^4 + 10^4) =41.498 * 10^4 Homework Equations this is an an example given in my TEAS (standardized skills test) work book/study guide...is it accurate? i don't know why (10^4 + 10^4) = 10^4 after the simplification The Attempt at a Solution
  43. M

    Sine Wave Addition: Standing Waves?

    If two sine waves have the same frequency and amplitude but have different phase shift do they still produce a standing wave? Thanks for the help.
  44. S

    Nyquist stability. Vector addition. Bad diagram?

    This isn't exactly coursework, since I am no longer in school, but I think this may be the most appropriate forum to post in. This link is for a TI/Unitrode app note, "Control Loop Cookbook", which is about control loops for switching converters...
  45. D

    Simplify Exponents and Confirm with Wolfram Alpha: (54-3y)3 * (5y-2)2 Solution

    So I just got back from my math class, we were going over exponents. Right before we left he gave us a problem and we turned it in, I was just wondering if I got it right. Simplify: (54-3y)3 * (5y-2)2 I got: 512-9y3 * 5y2-4 5-9y3+y2+8 I applied the powers to the parenthesis, then...
  46. M

    Addition formula for f(x+y) using mean-value theorem

    Homework Statement suppose f and g are two differentiable functions with f(0)=0, g(0)=1 and f'(x)=g(x) and g'(x)=-f(x). For a fixed y in R put F(x) = f(x+y) - f(x)f(y) - g(x)f(y) Compute F'(x) and F''(x) Then let E(x) = [F(x)]^2 + [F'(x)]^2 Apply Mean Value Theorem to E and...
  47. Kawakaze

    How to Calculate Magnetic Field Strength Between Parallel Wires

    Hi everyone, long time lurker, first time poster. Can someone please clear this up for me? Two wires running parallel to each other. I think its just an algebraic addition of the usual B(r)=u_0i/2pir but instead of r, we are using D and d aslso i apologise for my formulae, if someone...
  48. F

    What is the Einstein Velocity Addition Formula and How Does It Work?

    http://hyperphysics.phy-astr.gsu.edu/Hbase/relativ/einvel.html#c1 ok, so I'm looking at this, and i see that where c = speed of light if ship A is moving at .7c to the right ===> <=== and ship B moving .7c to the left and they are both on the same line and about to collide, at...
  49. O

    Relativistic Velocity Addition

    Homework Statement Nevermind, got it. Two spaceships approach the Earth from opposite directions. According to an observer on the Earth, ship A is moving at a speed of 0.753c and ship B at a speed of 0.851c. What is the speed of ship A as observed from ship B? Of ship B as observed from ship...
  50. S

    Spin states of the addition of 2 spin 1/2 particles

    Hi everyone, A QM question that I am stuck on: Consider the addition of the spin of 2 electrons, s1=s2=½. Show that there are one ms=1; two ms=0 and one ms=-1 states. Show the 4 spin states are given by: a1a2 b1b2 (1/(sqrt(2)))(a1b2+b1a2) (1/(sqrt(2)))(a1b2-b1a2) I've used a...
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