Addition Definition and 651 Threads

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. K

    Add 3 Vectors: Mag & Dir Calculations

    Homework Statement Three vectors, A, B and C each have a magnitude of 50 units. Their directions relative to the positive direction of the x-axis are 20°, 160° and 270°, respectively. Calculate the magnitude and direction of each of the following vectors. a)[/B]→A+ →B+ →C b)→A− →B+ →C c)2 (...
  2. P

    Generalized velocity addition and aberration formulas

    Not sure if this will be of interest to others, but, as an exercise, I decided to derive formulas for SR velocity addition for any angular relationship, and similar aberration of angle for any object speed and direction and observer relative velocity - using pure algebra/geometry. That is, no...
  3. C

    What is the value addition of GR?

    What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same. I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of...
  4. jove8414

    Vector Addition: Find the Resultant Vector

    Homework Statement [/B] The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint...
  5. J-dizzal

    What is the Magnitude of Betty's Force for Equilibrium?

    Homework Statement FC of magnitude 188 N. Note that the direction of FC is not given. What is the magnitude of Betty's force FB if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium Homework Equations ΣF=0[/B]The Attempt at a Solution...
  6. V

    What are the mathematical rules for adding consecutive numbers and squares?

    I have recently discovered some mathematical rules by trial and error. Some of these may be already known to people of mathematics. 1. This one is common: Sum of all integers 1+2+3+...=0.5(n^2 + n) 2. Sum of odd integers: 1+3+5+7+9...= n^2 3. Sum of even integers: 2+4+6+8...= n^2 + n eg...
  7. suraj 27

    Heat addition process in dual cycle

    why in dual cycle heat addition at constant volume process is first then after heat addition at constant pressure process is done?
  8. T

    Vector Addition Help (given heading and distance)

    Homework Statement To avoid restricted airspace, a pilot on a VFR cross country flight plans the following 3 legs immediately after takeoff. Leg A (280 heading 40nm distance) Leg B (240 heading 30nm distance) Leg C (200 heading 25nm) What one heading and distance from takeoff would...
  9. L

    What courses to take in addition to engineering physics?

    Hey, I am strongly thinking of switching from mechanical engineering over to engineering physics. I am thinking of taking the first year again, and will therefore have about 5 courses I can choose freely. So the question is, what courses could be a nice addition to a engineering physics degree...
  10. J

    Addition of Velocities Special Relativity Problem

    [Mentor's note: this post does not use the homework template because it was originally posted in a non-homework forum.] ----------------------------- A ship (attached to reference frame S') is passing us (standing in reference frame S) with velocity v= 0.933c. A proton is fired at speed...
  11. V

    Simple vector addition question

    Two cars approaching each other with speed 100km/h each. Relative to one of the cars the road moves with the speed of 100km/h (car pulls it toward itself), the other car moves on the moving road, vectors add - relative velocity 200 km/h just the way it should be. Relative to the road two cars...
  12. R

    Addition Series: Sum of Successive Terms

    Homework Statement I want to have a formula of this kind, (8+7+...+1) + (7+6+..+1) + (6+5+..+1) + ...1Homework EquationsThe Attempt at a Solution I know , n+(n-1)+...+1 = n(n+1)/2
  13. T

    Velocity Addition for Orthogonal Boosts in SR

    Hi, is there any general formula to find out the final velocity w, happened by a boost in x direction forst and then to y direction? I could find the boost matrices for both and I know it's not purely another boost, rather a boost and a rotation, but I am really confused which formula to use...
  14. K

    How good is HCN addition to aromatic conjugated aldehyde?

    Reaction of HCN with an aldehyde has higher yield than HCN with a ketone due to steric strain around the ketone. Then how about reaction yield of HCN with an aromatically conjugated aldehyde (like Ph-CHO) comparing with the previous two reactions? What I think: The yield be lower than just...
  15. ches18

    How to Discuss Grade Discrepancies with Your Professor

    Is it possible guys to add it that way? Well what i did is that i add the current sources even tho they are not parallel because of the voltage source... But it can be considered a node the upper part if you use super node... The one that is encircle is done by my prof... saying I'm wrong... but...
  16. D

    Addition property of integration intervals proof

    First of all, apologies as I've asked this question before a while ago, but I never felt the issue got resolved on that thread. Is it valid to prove that \int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx using the fundamental theorem of calculus (FTC)?! That is, would it be valid to do...
  17. Quarlep

    Einstein Velocity Addition for Relative Speed Calculation

    Lets suppose we used Einstein Velocity Addition equation and we found a result this is the same for every observer isn't it ?
  18. N

    Is Absolute Space and Time Really Absolute?

    Imagine two space ships each with thrusters that can accelerate them .1c or .3c almost instantly. The velocity addition formula indicates that if one spaceship applied the .1c thruster 3 times then if c is estimated to be 300,000,000 m/s the velocity of the ship after the accelerations the ship...
  19. G

    Numerical Approximation and addition of new data points

    Hi I am new member and I am new to the Signal processing so I hope I could get some help from the members to able to understand the concepts. I have a Signal. I have a 10Msaples/sec ADC. I view the Signal on an Oscilloscope which has 20Gsamples/sec sampling rate. The Point where I am...
  20. H.D. M A K

    When magnitude of addition is equals to

    Mod note: Originally posted in a technical math forum, so missing the homework template. How to find angle between two vectors when magnitude of both vectors and their resultant is given. for example The resultant of two vectors of magnitude 3n & 5n comes out 7N, the angle between vector is...
  21. H.D. M A K

    When magnitude of addition is equals to

    When magnitude of addition is equals to the magnitude of difference of two vectors then the angle between them will be 90 degrees... How and Why ? can anyone explain it ?? Any help will be appreciated.. Thanks
  22. Coffee_

    [QM] Addition of spin for normal and identical particles

    1. Problem: Consider the composed system of two particles of spin ##s=1## where their angular momenta is ##l=0##. What values can the total spin take if they identical? What changes when they are distinguishable? The Attempt at a Solution : The problem I have here is incorporating the fact...
  23. C

    Finding Equilibrium in a Three-Pulley System

    Homework Statement Place 0.150kg (including the mass of the hanger) at a position somewhere between 0 degrees and 90 degrees. (I chose 45 degrees for this problem.) Place the second pulley at exactly 180 degrees and the third pulley at exactly 270 degrees. Determine how much mass you must place...
  24. J

    Vector Addition Problem - Statics

    Homework Statement Find the magnitude and direction of the resultant force Fr=F1+F2+F3 by first finding F'=F1+F2 then Fr=F'+F3 known values are in the link Homework Equations Basic vector addition. Law of cosines. Law of sines. The Attempt at a Solution Here's my attempt. I'm not convinced by...
  25. R

    Vector Addition: Which Statement is True?

    Homework Statement The diagram shows 3 vector all of equal length. Which statement is true? a. A+B=A-C b. A+B=B-C c. A-B=2A-C d. A-B=2A+C e. 2A+2B=2C Homework Equations None The Attempt at a Solution I just added them in my head, and thought that e. 2A+2B=2C would also work. Why doesn't it?
  26. S

    Vector Addition/Components Problem

    Homework Statement I am having difficulties in analyzing problems. Here are the problems: A1. A hiker begins trip by walking 25km southeast from her base camp. on the second day, she walks 40km in a direction of 60 degrees N of E, at which point she discovers a forest ranger's tower. Determine...
  27. R

    Vectors Addition Homework: Plane Path Problem

    Homework Statement [/B] A plane flies the following paths: 168 km to the Northeast, 144 km to the Southeast, 246 km to the Southwest, and then 127 km to the Northwest. At the end of the trip, how far was the plane from the original airport? Homework Equations [/B]Pythagorean theorem...
  28. A

    Understanding Limits: Addition and Multiplication Rules

    (I have posted this in this section, rather than homework, because I hope to improve my general understanding of methods of finding limits through these problems.) 1: \lim_{x\rightarrow0} (\frac{cosec(x)}{x^3} - \frac{sinh(x)}{x^5}) I don't really know what to do with this one. I tried...
  29. T

    Exchange symmetry and addition of angular momentum

    In case it's relevant, the context of my question is finding the allowed states of an atom. For example, given a nitrogen atom with (1s)2(2s)22p3, how do we find the possible states in terms of total orbital angular momentum L, total spin S, and total angular momentum J = L + S. It seems that...
  30. S

    MHB Lightning Addition: Master the Art of Mental Math

    . . . . . Lightning Addition Give your volunteer a sheet of paper, a pencil and a calculator. Then give him these instructions. Number the lines 1 to10. On the first line, write any one-digit number. On the second line, write any one-digit number. On the third line, write the sum of the 1st...
  31. H

    Is Addition Associative? A Proof Using Induction

    Homework Statement For any natural numbers a,b,c, we have (a+b) + c = a + (b + c) Homework Equations Definition 2.2.1 Let m be a natural number. To add zero to m, we define 0 + m := m. Now suppose inductively that we have defined how to add n to m. Them we can add n++ to m by defining (n++) +...
  32. DataGG

    Addition of angular momentum - Finding the second tower states

    Homework Statement I'm supposed to calculate all the states for a system with ##l=1## and ##s=1/2##. Let's say ##\vec{J} = \vec{L} + \vec{S}##. I want to find the Klebsch-Gordon coefficients. I know that said system has 2 towers, one with ##j=3/2## and the other with ##j=1/2##. I've...
  33. P

    Addition Rule for Random Variables

    Hi, I am having a hard time understanding why the Addition Rule for two Random Variables holds even when the random variables are dependent. Essentially: why is E(X+Y) = E(X) + E(Y) when X and Y are dependent random variable? Given the two variables are dependent, if X happens to take on a...
  34. D

    What Are the Major Products of These Organic Addition Reactions?

    1. What is the expected major product arising from the reaction of 2-ethylbut-1-ene with bromine in carbon tetrachloride? a. 1-bromo-2-ethylbutane b. 2-bromo-2-ethylbutane c. 1,2-dibromo-2-ethylbutane d. 1,1-dibromo-2-ethylbutane e. 1,1,2-tribromo-2-ethylbutane Attempt: For this one I'm...
  35. M

    Three Reference Frame Relativity Problem - Velocity Addition or Proper Lengths

    Homework Statement Anna and Bob have identical meter sticks. Anna an observer on Earth, sees Bob traveling in a spaceship at 0.5c away from her. Bob leaves his spaceship in an escape pod, moving away from Earth and the spaceship at 0.1c with respect to the spaceship. How long is Bob's meter...
  36. J

    How do I add vectors using geometric and component-wise methods?

    Homework Statement Hello, this is my first time taking physics in college, and I have read the section twice and I this is what I understand. If someone could point me in the right direction, that would be great. For example: How do I find the angle for example from Vector a + Vector b. Would...
  37. DiracPool

    Relativistic velocity addition

    I feel I understand relativistic velocity addition fairly well. However, the way I usually see it modeled is with two travelers moving in the same direction. Bob is in a spaceship traveling at 0.6c and shines his flashlight in the direction of travel. An inertial observer, Alice, relative to...
  38. K

    Why does the + sign move to O in the addition of alkene with water?

    Homework Statement my question is at part 2 , since c form ch3ch2 is electron deficient, but after OH2 added in , with lone pair electron on O, the c should be no longer electron deficient anymore. am i right? why the + sign is moved to O now? Homework Equations The Attempt at a...
  39. A

    Is There a Mistake in Calculating Vector Components and Angles?

    There seems to be problem with the answer to this problem. Weirdly, they get that the x component of F1 is 3N! Then, when they end up calculating the direction in C, they get 9.5°. I get 9.16°. Am I the one going crazy? This is fairly straight-forward!
  40. N

    MHB Why is sin(3pi/2) not equal to 1?

    What exactly does it mean for something to be closed under addition. most of the examples and questions i have gone past, are answered with u + v = u1+v1, ... , u_n + v_n and hence this is closed under addition. So i tried looking for examples where something was not closed under addition...
  41. A

    Relativistic velocity addition and signs

    Hello all, I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really illuminating in some aspects, I still feel that regardless of how hard I try there is...
  42. 1

    Relativistic addition of velocities problem

    Homework Statement You are driving down a two-lane highway and a truck in the opposite lane travels toward you. Suppose the speed of light in a vacuum is 65 m/s. Determine the speed of the truck relative to you when a - your speed is 25 m/s and the truck's speed is 35 m/s and b - your...
  43. D

    Why does nitrogen gas' pressure not change after an addition of helium

    a 9 L vessel contains 3 moles of helium and 3 moles of nitrogen at a pressure of 10 atm. Maintaining constant temperature, an additional 2 moles of helium are added. Assuming gases behave ideally, what are the partial pressures of nitrogen and helium at the end? Initially there's: 3mol He/(3mol...
  44. U

    Two spin-1 objects: Addition of Angular Momenta

    Homework Statement Suppose in a container there are two spin-1 objects, A and B. It is found that ##J=j_1+j_22## and ##M=m_1+m_2=1##. What is the probability when ##J_z## is measured for A, values of m=0, m=-1 and m=+1 will be obtained? Homework Equations The Attempt at a Solution |j,j> =...
  45. U

    Addition of Angular Momenta - Degeneracy

    Homework Statement Show that when angular momenta ##j_1## and ##j_2## are combined, the total number of states is ##(2j_1 +1)(2j_1+2)## Homework Equations The Attempt at a Solution For the two gyros in the box, there are ##2j_1 +1## possible orientations of the first gyro...
  46. S

    Why does heat addition happen at constant pressure in diesel cycle ?

    Why does heat addition happen at constant pressure in diesel cycle ? what is the basic concept behind it?? please do enlighten me on this topic. thanks in advance
  47. AwesomeTrains

    Finding the Dimension of the Union of Subspaces

    Evening everyone, I have a problem with addition of subspaces. Homework Statement I have to find the dimension of U and dim(V), of the union dim(U+V) and of dim(U\capV) U is spanned by \begin{align} \begin{pmatrix} 1 \\ -2 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 \\...
  48. S

    Vector addition of gravitaional , magnetic and elctrical field

    can we consider gravitational field, magnetic field and electrical field as vector? can see the net result of this field.
  49. M

    Combining Sine Waves: Adding 2 sin (314.2t) and 2 sin(314.2t - 120°)

    I need to add together the following sine waves and express the answer in the same form: Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°) Any help would be greatly appreciated.
  50. Y

    Understanding Vector Addition and Magnitude Equality

    Homework Statement If vector A + vector B = vector C and magnitude A + magnitude B = magnitude C how are vector A and B relative to each other. Homework Equations The Attempt at a Solution I need help understanding this question. I know that in order for them to be equal they...
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