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

    Addition and multiplication in Z/nZ

    I need to show that addition and multiplication are well-defined in Z/nZ. So far, I've figured out that I need to work within this framework: Suppose a ~ a' and b ~ b'. Try to prove a + b ~ a' + b'. If a ~ a'...something If b ~ b'...something Any ideas?
  2. S

    Propagation of errors addition numbers without uncertainty

    Homework Statement I am having trouble calculating uncertainty when a number is added to a value with uncertainty. M = 350g a = 0.624 \pm 0.001 µk = 0.07 g = 9.80 m/s2 Homework Equations T = M*a + µk*M*g The Attempt at a Solution T = (350g)*(0.624 m/s2) +...
  3. A

    How Do You Calculate the Combined Phase Angle Shift of Multiple Waves?

    Homework Statement If I have three different waves each with difference amplitude and phase angle how would i find the combined phase angle shift? wave 1: A=5 phi=0 wave 2: A=5 phi=pi/4 wave 3: A=9 phi=pi/2 Homework Equations phi'=arctan(a2sin(phi)/(a1+a2cos(phi)), where phi in...
  4. N

    Vector addition and Relative motion

    Homework Statement 1) A boy is floating on a raft in a river. THe water flows at a speed of 12m/s east. The boy's feet kick the water,causing a velocity of 2m/s at an angle of 43 degrees north of east. Using Vector components, calculate the magnitude of the raft's velocity. 2)One vector...
  5. P

    Significant Figures addition & conversion

    Having a discussion with a colleague over sig figs and conversions. Original problem: find perimeter of 12.6 ft by 13.88 ft room and express answer in meters. 16.1 m or 16.2 m? Question is when to round? After finding perimeter in feet? 53.0 feet to meters = 16.2 meters or at the...
  6. O

    How to Plot a Standard Addition Curve.

    Homework Statement The concentration of cadmium in seawater can be determind spectrophotometrically. To six 50.0mL seawater samples, various volumes of a 10.0ppm cadmium solution were added and all were taken through the analytical procedure with the following results: Amount Cd Added...
  7. W

    Resultant Gamma after Einstein velocity addition

    Hello. Let's say that I am in a frame in which I see a rocket traveling at v. This rocket then fires a projectile forward with velocity u in its rest frame. I can find u' easily enough using the Einstein velocity addition formula. However, I recall seeing a version of the formula that uses...
  8. A

    Add Vectors: Angle & 3-Phase Systems

    how to add two vectors knowing only angle between them for example if we have two vectors A and B having angle 40 degrees what will be the resultant sum of two? also in three phase systems how to find resultant of two voltage of equal magnitude having a phase difference of 120 degrees
  9. J

    Calculating Distance and Direction Between Two Teams in a Remote Area Using GPS

    Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 38 km away, 19° north of west, and the second team as 29 km away, 35° east of north. When the first team uses its GPS to check the...
  10. J

    How Do You Calculate Resultant Velocity in Vector Addition?

    Homework Statement A plane heads 20° north of east at 200 m/s. The wind blows 60° north of east at 50 m/s. What is the resultant velocity of the plane? Homework Equations Δv= v2-v1 or Δv= v2+(-v1) The Attempt at a Solution I know you have to solve for the x and y, but I don't know...
  11. E

    Few Vector Addition questions, Not sure if correct

    Homework Statement 1) Two men are near a hole, One man walks 12m east and then 12m North from a hole, the other walks 15m west and then 11m north, Find the dot product of their net displacements from the tree _______ 2) Vector A = -i +2j - 5k, Vector B = 3i +2j -2k Find the magnitude...
  12. C

    Addition of bearings (Eastings/Northings)

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  13. E

    Vector Addition Problem: How Far and In What Direction Did the Hiker Travel?

    Homework Statement [PLAIN]http://img6.imageshack.us/img6/4057/pictureforforums.png A hiker walks 8.33 km 30 degrees N of E then 4.97 km 45 degrees N of W and finally 7.32 km 60 degrees S of E. How far and in what direction is the hiker from the original position (A) to (B) Homework...
  14. E

    Modular Arithmetic proofs (multiplication and addition mod n)

    Homework Statement Let n be a fixed positive integer greater than 1. If a (mod n) = a' and b (mod n) = b', prove that (a+b) (mod n) = (a'+b') (mod n) and that (ab) (mod n) = (a'b') (mod n) Homework Equations When a = qn + r a mod n = r The Attempt at a Solution (a'+b') (mod n) = (a...
  15. 1

    How Do You Add Vectors Using Unit Vector Notation?

    Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...
  16. B

    How Does Rotating the x-Axis Create a New Polynomial Graph?

    To show the addition of the term mx to a polynomial graph, my book takes an example with y=x^3. To produce a function y=x^3 - 3x it draws the graph of y= x^3. Then the line y= - 3x is drawn in the same graph. quote" If we think of the ordinates of y=x^3 as attached to the x-axis and constrained...
  17. E

    Vector addition with 4 force vectors

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  18. jfy4

    Addition for generators of rotation

    Hi, I have here the following rules for representations of the Lorentz algebra including spinors The representations of the Lorentz algebra can be labeled by two half-integers (j_{-},j_{+}). The dimension of the representation (j_{-},j_{+}) is (2j_{-}+1)(2j_{+}+1). The generator of...
  19. N

    Spherical Vector Addition Process

    Hello Everyone, I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I...
  20. S

    (LinearAlgebra) all 2x2 invertible matrices closed under addition?

    Homework Statement Suppose V is a vector space. Is the set of all 2x2 invertible matrices closed under addition? If so, please prove it. If not, please provide a counter-example. Homework Equations The Attempt at a Solution well i know that what does it mean to be closed...
  21. K

    Addition and Multiplication of functions with radicals in the denominator

    Homework Statement f(x)= 1/(5x2 +3) g(x)=1/(x-2)1/2 find (f+g)(x)The Attempt at a Solution for (f+g)(x) I use the common denominator by multiplying each side by (x-2)1/2/(x-2)1/2 and (5x2 +3/5x2 +3) respectively. I end up with a whole mess that I am unable to rearrange into anything useful...
  22. A

    Addition of exponentials, and relationship between variables.

    Homework Statement This is, strictly speaking, not a homework question. I have already solved this, but I think that there is a much better method to solve it. In the equation below, what relationship must w and q satisfy? If the question is not clear, please read the bottom of the post...
  23. P

    Relativistic addition of orthogonal velocities

    Homework Statement In a given inertial frame, two particles are shout out simultaneously from a given point, with equal speeds v, in orthogonal directions. What is the speed of each particle relative to the other? Answer: v{(2-\frac{v^{2}}{c^{2}})}^{1/2} Homework Equations Velocity...
  24. L

    Finding Magnitude and Direction of Vector Addition and Subtraction

    vector A has a magnitude of 81 units and points due west, while vector B has the same magnitude and points due south. Find the magnitude and direction of (a) A + B and (b) A - B . Specify the directions relative to due west. (a) Magnitude and direction of A + B = and o (b) Magnitude and...
  25. A

    Vector Addition Problem: What is the Fourth Vector?

    Homework Statement a person goes 180 m due west then 210 m 45 degrees east of south then 280 m 30 degrees east of north. After a fourth displacement the person is back where they started. what is the fourth vector? The Attempt at a Solution So I first added the first two vectors of 180...
  26. A

    How Do You Calculate Vector Sums and Differences?

    Homework Statement find the vector sum of A + B. Find the vector difference of A-B. Then find the magnitude and direction -A-B and B-A. Vector A=12m and B=18m and the angle between B and the x-axis is 37 degrees. I'm really confused about how to think about a vector and if i should just...
  27. S

    Stability of the gaussian under addition and scalar multiplication

    If i have the mgf of X and the mgf of Y where X~N(mx,vx) and Y~N(my,vy) and X and Y are independent , then if i want to show that aX +bY ~ N(amx+bmy , a^2vx+b^2vy) how would i do this - need to be able to do the convolutions way and the mgf's way, for the mgfs way is it just, mgf(ax+by) =...
  28. G

    Addition of Reluctances in Parallel [MAGNETISM]

    Homework Statement Hey guys, I have an incredibly broad question, just revising the topic of Magnetism, On the topic of reluctance, As I have learned so far, Magnetic Circuits and electric circuits have similar properties. When the core is a "series" network, you add Reluctance together...
  29. M

    Troubleshooting Signal Addition Using Opamp: A Case Study

    Hey guys, first of all this is my first post in here so I hope I am doing the procedure of asking questions the right way. My problem is; I want to add two signals and generate a 1.5 period of sinusoidal wave only at the beginnig. It will be a sine wave starting at t=0 and ends at t=1.5T...
  30. D

    Vector addition - Vector Spaces

    Homework Statement Show if V is a vector space ([a,b,c]|ab>=0). I'm trying to test whether it is closed under vector addition. Homework Equations v=[a1,b1,c1] w=[a2,b2,c2], v and w satisfy ab>=0 a1b1>=0, a2b2>=0 show (a1+a2)(b1+b2)>=0 The Attempt at a Solution Got to a1b1...
  31. D

    How does colour addition / subtraction work?

    I am familiar with the ideas of colour subtraction and addition, such as adding blue and yellow to make green. However, how does this work from an electromagnetic standpoint? Is there basis for the addition or subtraction, or averages, of the wavelengths or frequencies? Is the colour change a...
  32. O

    Angular momentum addition in quantum mechanics

    Homework Statement There is a combined system with angular momenta j_{1}=\frac{1}{2}, j_{2}=\frac{3}{2} and j_{3}=1. The Hamiltonian of the composite system depends only on the total angular momentum. What are the states of the combined system? What are the degeneracies of the eigenenergies...
  33. L

    Adding Velocities: Formulas & Calculations

    When adding velocities how do you know whether to use formula of the form w=\frac{u+v}{1+\frac{uv}{c^2}}, derived from using lorentz transformation, and when to use w = c sqrt[c^2(u-v)^2-u^2v^2+(u.v)^2]/(c^2-u.v) derived using four velocities? thanks
  34. H

    Lie Algebra of the reals with addition

    The following question may be trivial, but I just can't get it figuered out: Consider the real numbers R with the addition operation + as a Lie Group (R,+). What is the Lie Algebra of this Lie Group? Is it again (R,+), this time considered as a vector space? If so, what is the exponential map...
  35. K

    If we have two parallel plane in the space in addition to another two

    If we have two parallel plane in the space in addition to another two objects moving in parallel with the same velocity .what is the time for both. i mean does the time differe?
  36. O

    Angular momentum addition and expansion in states

    Homework Statement Part (e) of the attached question. Sorry for using a picture, and thanks to anyone who can help. Homework Equations the answer to part (d) is that the eigenvalue is \hbar^{2}\left(l\left(l+1\right) + s\left(s+1\right)+2m_{l}m_{s}\right) where, for this part of the...
  37. B

    Proof of the Addition Identies

    So throughout this entire semester in my Precalculus class my instructor told us that for solving trigonometric formulas, we will only learn about using these three formulas: sin2θ + cos2θ = 1 sin(A+B) = sinAcosB + cosAsinB and cos(A+B) = cosAcosB - sinAsinB For about two months we've...
  38. T

    Addition of 3d force vectors to find resultant

    Homework Statement A force of 5N acts along the vector (-4,-3,-1) A force of 2N acts along the vector (-3,-6,5) A force of 4N acts along the vector (-9,-1,8) find the resultant force vector. Homework Equations The Attempt at a Solution i tried to multiply the vectors by the...
  39. N

    Addition of velocities. relativity.

    Homework Statement Show that the addition of velocities implies that: a)if V < c in any inertial frame, then V < c in any other. b)If V=c in one inertial frame, then V=c in the other. c)If V>c in any inertial frame, then V>c in any other inertial frame. Homework Equations...
  40. E

    Resources for Addition Taylor Series/Approximations Problems

    First off, I apologize if this is in the spot. I thought about this off and on since this morning on where to put it. There are probably four sections this could go. Feel free to move it if needed. I am awful at recognizing and solving taylor series and approximation type problems. Since...
  41. T

    Addition of Angular Momentum - Measurement Probability

    Say we have two particles with angular momentum basis states |j_1~m_1\rangle and |j_2~m_2\rangle and the combined system is in the state: |0~0\rangle=\sqrt{\frac{1}{6}}\left(|1~1\rangle |1~-1\rangle+|1~-1\rangle |1~1\rangle\right) What is the probability that measurements of the...
  42. J

    Vector Addition and Displacement Magnitude in 3D Space

    Homework Statement The summit of a mountain, 2450m above the base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4 degrees west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x-axis...
  43. A

    Electrophilic addition of alkenes

    In reaction of alkenes with bromine water the electrophile Br+ has the first chance to attack(form a ring cabocation-like species). But the second anti attack(of the nucleophile) is attributed to water instead of Br-. Can somebody tell me why? Because water is stronger nucleophile? And why...
  44. G

    Calculating Velocity from Vector Addition of Ion Positions

    Homework Statement An ion's position vector is initially r> = (5.0m)i - (6.0m)j = (2.0m)k and 10 s later it is r> = (-2.0m)i +(8.0m)j - (2.0m)k. In unit-vector notation, what is its during the 10 s? The answer is supposed to be r> = (-0.7m/s)i + (1.4m/s)j - (0.4m/s)k (from back of my book) but...
  45. M

    Addition formulae proof for sin(x + y) and cos(x + y)

    For a fixed y \in R , if f(x) = [sin(x+y)]-(sin x) (cos y) − (cos x) (sin y)and we let E(x) = [f(x)]^2+[f'(x)]^2. How do we prove the addition formulae for sin(x + y)and cos(x + y) by applying the Mean Value Theorem to E
  46. S

    Vector Addition - Grade 12 part 3

    Homework Statement A new pilot with Canjet is asked to find the resultant displacement of his jet if it flies at 345km/h @ 225 degrees into a wind that is blowing at 40km/h from the West. Use the 'construction line' method, components method, AND law of sines and cosines. Homework...
  47. S

    Vector Addition Problem: Finding Final Displacement using Law of Sines/Cosines

    Homework Statement A land surveyor walks 5200m @ 330 degrees and then turns and goes an additional 3000m @ 180 degrees. Find his final displacement using the law of sines/cosines. Homework Equations I know the law of sines is a/sinA = b/sinB = c/sinC, and the law of cosines is a^2=b^2...
  48. P

    Vector addition. finding x & y components, the magnitude, & the angle

    Homework Statement Two vectors have equal magnitude of 14.8 m and the angles are theta 1 = 32 deg & theta 2 = 108 deg. Find a) their x component b)their y component of vector sum \vec{}r c) the magnitude of \vec{}r & d) the angle \vec{}r makes with the positive direction of the x axis...
  49. S

    Vector addition and subtraction

    1. Vector A has a magnitude of 14 m and makes an angle of 26o with the positive x axis. Vector B also has a magnitude of 13 m and is directed along the negative x axis. Enter your answers in distance then angle(in degrees). 2. Find A + B Find A - B 3. 14cos(26)=12.6 x component for A...
  50. P

    Solving Addition of Vectors Problem: Peter G's I.B Physics High Journey

    So, I started my I.B Course for Physics High and we've took off with a simple subject, addition of vectors. We finished it today but the last question was quite hard. I had a try, asked the teacher but the thing is I can't understand what the problem asks for, or how to approach the problem...
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