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. T

    Is my 2's complement addition correct?

    Do the following additions in 8-bit binary two's complement: a) 01110110 + 10001001 = (64+32+16+4+2) + (-(64+32+16+4+2+1)) = 118 -119 = -1 b) 11010101 + 10101010 = -(64+16+4+1) + (-(64+16+4+1+1)) = -86 -87 = -171 Have I done these correctly?
  2. W

    Desk addition for raising and lowering monitor/keyboard/mouse setup

    I'm looking to build my own desk addition that will allow me to raise and lower my work setup (keyboard, mouse and monitor) any time I like and with a fair amount of ease. I was inspired by the "Ergotron Workfit" but find the price tag beyond my range for now. Attached is a laughably...
  3. S

    System under matrix addition (+) and matrix multiplication (.) is a field

    Homework Statement true or false .. The system {S,+,.} with S = { matrix (a,b,a-b,a)|a,b ∊ R) is not a field under matrix addition (+) and matrix multiplication (.) i find that the statement is false . since : 1. {S,+} is Abelian group. 2. {S,.} : is Abelian group. is...
  4. V

    Can Eigenvalues of Matrix Addition Be Simplified?

    Hello, I have a linear algebra problem that I need help with. Basically, I need to get the eigenvalues and eigenvectors of several (sometimes tens of thousands) very large matrices (6^n x 6^n, where n>= 3, to be specific). Currently, we are just using MATLAB's eig() function to get them. I...
  5. I

    Are Undefined Matrices Additive in This Homework Problem?

    Homework Statement DB+CA^T-2A D=3row x 3col B=2x2 C=2row X 3col A=3row X 2col The Attempt at a Solution It is my understanding that a row of a matrix is horizontal variables and a column is the vertical variables. And for multiplication of two matrices you need the colums of...
  6. W

    Addition of Velocities: A photon emitted backwards

    So I just finished learning about the derivation of the addition of velocities...this should imply that I am a newcomer to relativity. So here's my question: We have a rocket that is traveling away from a lab at the relative velocity of c. (I know this is impossible because it would take...
  7. V

    Addition of grav potentials / Orbital velocity

    The Attempt at a Solution I think I may of been too general with the volume in finding M_0 I'm assuming r_0 = r_M although I'm not sure why different notation is used thougj http://imageshack.us/photo/my-images/3/gravscan.jpg/
  8. V

    Which will give better neuclophilic addition reaction?

    Initial Compound is like this Ph---CO---O----CO----CH3.(Ph means phenyl) It is reacted with H3O+. What will be product? I think first attack will be at carbonyl carbon near methyl. Because phenyl ring will donate electrons to carbonyl group near it and make it less attractive towards...
  9. M

    Finding the Angle Between Two Vectors with Equal Magnitudes

    Homework Statement Vectors A and B have equal magnitudes of 10.0. If the sum of A and B is the vector 3.13j , determine the angle between A and B Homework Equations none The Attempt at a Solution I gave both A and B the length r=10 I don't know how to add them together if I don't...
  10. N

    Vector Addition Homework: Find F2 Magnitude & Direction

    Homework Statement There are two forces on the 3.2 kg box in the overhead view of the figure below but only one is shown. The figure also shows the acceleration of the box. F1 is in Q I and F2 is in Q III a = 12m/s2 there is a picture here that I do not know how to upload -- it shows F1 in...
  11. B

    Addition of 2-D vectors and relative velocity

    Homework Statement A plane must fly to a destination located due north from its departure point. A gentle wind is blowing from the south-west. What direction must the plane point to reach its destination? Homework Equations The Attempt at a Solution...
  12. F

    Physical equivalence of Lagrangian under addition of dF/dt

    Homework Statement This isn't strictly a homework question as I've already graduated and now work as a web developer. However, I'm attempting to recover my ability to do physics (it's been a few months now) by working my way through the problems in Analytical Mechanics (Hand and Finch) in my...
  13. A

    Adding Normal Forces for Net Force Calculation

    Homework Statement How do you add the normal forces together after you derive the x and y component? Homework Equations Normal force = m*g*sinθ (y component) Normal force = m*g *cosθ (x- component) The Attempt at a Solution Bottom line is I'm trying to get the Net Force...
  14. J

    MIPS programming successive addition

    Homework Statement I need to create a program that will prompt for two integers, echo those integers, and then multiply them without using the multiplication operation and report the result. Homework Equations The following is what I have so far. The prompts and echoes work, however I do...
  15. M

    Help Proof of simple theorems with addition and mulitplication axioms

    Thanks in advance. 1st day at calculus teacher wants proofs. They seem rudimentary but I've never done them and he doesn't help so I'm hoping someone here could please. These are the axioms: Addition: For a, b, and c taken from the real numbers A1: a+b is a real number also (closure) A2...
  16. H

    Vector Addition Homework: Magnitude and Angle Calculations

    Homework Statement Two vectors are given by a = 2.3 x - 9.7 y and b = -18.6 x + 2.8 y. What is the magnitude of a? What is the angle between vector b and the positive x-axis? What is the magnitude of the vector a + b? Homework Equations I don't know The Attempt at a Solution...
  17. E

    Trouble with basic Vector Addition Problem

    This a book example that I have the answer to but do not understand. What are the magnitude and direction of the total displacement for the treasure hunt? The instructions to find the treasure are 5 paces North, 3 paces East, then 4 paces Southeast. Each pace is 0.750 m in length. So I...
  18. R

    Addition of Complex Term in Lippmann Schwinger Equation

    Hello PF People, This is probably a very simple question but I don't really get it. In Lippmann Schwinger Equation we add an infinitesimal term to the denominator in order to avoid singularity for when E is an eigenvalue of \hat{H}_0. This is fine, but why it has to be a complex number...
  19. S

    Is this correct proving function addition is associative?

    Is this correct...proving function addition is associative? Homework Statement Let F be the set of all real-valued functions having as domain the set ℝ of all real number. Prove that function addition + on F is associative. Homework Equations The Attempt at a Solution I'm...
  20. Roodles01

    Vector addition; spherical coordinates

    Should be quite easy, really, given that it's just adding things together, hey ho. Problem a position vector of point (1), identified by sherical coordinates, is 5m away from point (2). I have a unit vector R1,2 identified by spherical coordinates [Aex - Bey +Cez], giving the direction to...
  21. S

    Addition and subtraction in machine language

    I'm working on an assignment for a computer science course. The professor did not give very good instruction, and I can't find very much information about the subject online. We are supposed to use this http://www.anne-gert.nl/projects/simpsim/ program to preform various operations including...
  22. U

    Velocity addition formula for multiple velocities within each other

    I am having a problem coming up with an empirical formula for multiple objects moving with the same speed relative to each one up. I.e. there is a cart moving with speed u relative to me, and inside it is a cart moving speed u relative to the cart is inside it. and inside that cart is a cart...
  23. T

    Intersection and Addition of Subspaces

    Homework Statement http://img824.imageshack.us/img824/3849/screenshot20120122at124.png The Attempt at a Solution Let S = \left\{ S_1,...,S_n \right\} . If L(S) = V, then T = \left\{ 0 \right\} and we are done because S + T = V. Suppose that L(S) ≠ V. Let B_1 \in T such that B_1 \notin...
  24. D

    Addition of vectors with triangle vertices

    Homework Statement If A, B, and C are the vertices of a triangle, find the following. (A→B) + (B→C) + (C→A) The answer has to be given like this: _____ i + _____ j 2. Homework Equations (I think?) a+b=b+a a+(b+c)=(a+b)+c a+0=a a+(-a)=0 c(a+b)=ca+cb (c+d)a=ca+da (cd)a=c(da)...
  25. T

    Intersections of Subspaces and Addition of Subspaces

    Homework Statement http://img824.imageshack.us/img824/3849/screenshot20120122at124.png The Attempt at a Solution Let S = \left\{ S_1,...,S_n \right\} . If L(S) = V, then T = \left\{ 0 \right\} and we are done because S + T = V. Suppose that L(S) ≠ V. Let B_1 \in T such that B_1 \notin...
  26. T

    Identifying Subspaces and Subspace Addition

    Homework Statement http://img21.imageshack.us/img21/4580/screenshot20120117at218.png The Attempt at a Solutiona) Suppose we have two arbitrary vectors of E, call them X,Y. Let X = (2x,x) where x is in R and let Y = (2y,y) where y is in R. If we add X and Y we have (2x,x) + (2y,y) =...
  27. T

    Proving Uniqueness in Subspace Addition

    Homework Statement http://img854.imageshack.us/img854/5683/screenshot20120116at401.png The Attempt at a SolutionSo we have that A + B is a vector in S + T, where A is an element of S and B is an element of T. Suppose there is another vector A' + B' also in S + T, where A' is an element of S...
  28. L

    Physics w/ Calculus, Ch. 1 question: Vector Addition

    This seems to be a very perplexing problem to which there is much difficulty of making sense of. So instead of trying to rewrite the problem in pieces, I've decided to provide the entire image leading up to the question so that you are seeing what I'm seeing. Hopefully, if I can describe where...
  29. T

    Proving Uniqueness in Subspace Addition

    Homework Statement http://img854.imageshack.us/img854/5683/screenshot20120116at401.png The Attempt at a SolutionSo we have that A + B is a vector in S + T, where A is an element of S and B is an element of T. Suppose there is another vector A' + B' also in S + T, where A' is an element of S...
  30. L

    H/W help on Geometric vs Component Vector Addition

    Homework Statement Find y component of vector C from its length and the angle it makes with the x axis, that is, from geometry. Express the y component of vector C in terms of C and \phi. Homework Equations Vector addition using geometry: 1) C = \sqrt{A^{2}+B^{2}-2ABcos(c)}...
  31. O

    Addition of Vectors using a scale diagram

    Homework Statement Add each set of vectors by using the scale diagram C=28km 20 degrees north of east; D=34 km 30 degrees west of north Homework Equations The Attempt at a Solution Attempted to create a triangle with a right angle; then Pythagorean
  32. A

    How does the addition of a weight change the speed of an air rising in water?

    Air rises in water at about one foot per second of time. If a container of air has a lifting force of 100 Lbs and rises at one foot per second what happens when a 10 lb weight is attached to it? What is its speed in the water then? What about 50 Lbs? or 90 Lbs? What is the speed reduction to...
  33. S

    Another Addition of Vectors question.

    Homework Statement Sudhir walks 0.40 km in a direction 60.0° west of north, then goes 0.50 km due west. What is his displacement? Homework Equations According to my textbook, the equations are: Ax = A cos θ Ay = A sin θ Bx = B cos θ By = B sin θ θ = tan-1 opposite side/adjacent side...
  34. S

    What is the displacement after traveling on two different compass headings?

    Homework Statement I set out on a compass heading of 15.0 degrees west of south for 23.4km. I turn 20.5 degrees east of south and travel another 32.0km. What is my displacement? Homework Equations I'm not sure if there are any. But these should help. Ax = A cos θ Ay = A...
  35. N

    Why is this idea on addition of velocities in SR wrong?

    I like to try and derive little things by myself if I think it is manageable. One such thing is the addition of velocities. I gave it a stab, got an answer, and it turned out to be wrong. So tell me where my logic messes up. There's a spaceship moving at velocity u1. A man in the spaceship...
  36. C

    Union and addition of two subspaces a subspace?

    Homework Statement This problem is broken into 5 parts: (1) Let E={(2a,a)|a∈ℝ}. Is E a subspace of R2? (2) Let B={(b,b)|b∈ℝ}. Is B a subspace of R2? (3) What is E\capB? (4) Is E\cupB a subspace of R2? (5) What is E+B Homework Equations E={(2a,a)|a∈ℝ} B={(b,b)|b∈ℝ} The Attempt...
  37. S

    Number question, addition and multipulcation

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  38. S

    Solving trig equations using Addition formula

    Homework Statement Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏ Homework Equations sinAcosB+cosAsinB The Attempt at a Solution sin(x+∏/6)=2cosx 2cosx=(√3)/2sinx+1/2cosx How do I solve from here?
  39. S

    Trig - Addition Formula Question

    Homework Statement Solve the equation cos(x-60)=sinx Homework Equations cosAcosB+sinAsinB The Attempt at a Solution cos(x-60)=sinx cosxcos60+sinxsin60=sinx 1/2cosx+(√3)/2sinx=sinx How do I then solve to find x for0<x<360
  40. K

    Vector Addition Help: Find Resultant of 5 Vectors

    Homework Statement Find the resultant for the following directions. 20 degrees east of south for 1/2" 80 degrees South of west for 5" 15 degrees west of north for 1" 35 degrees North of East for 3" 40 degrees South of East for 1"Homework Equations R2 = a2 + b2 The Attempt at a Solution i...
  41. L

    Necessary But Not Sufficient Check For Addition

    When I was in grade school my father told me about a method of checking my addition when I added columns of numbers. I hold degrees in mechanical engineering but none of my math courses ever broached this subject as it is pretty much useless for engineering type problems. Suppose you added...
  42. M

    Vector addition and subtraction. feeling stupid for being confused over this

    Homework Statement A = 2i + 3j B = -5i + 6j Calculate (draw vector diagram) A + B A - B Homework Equations actually we're just confused as to whether we need to use the angles to answer this or just answer it directly, meaning that for A + B the answer would be -3i + 9j The...
  43. I

    Software to demonstrate addition of SHO's

    Hi I am looking for a simulation software to demonstrate addition of waves with different amplitudes, frequencies , velocities. So I should be able to define , say , 2 to 3 component waves and the output will give me the addition of these waves. I think showing actual simulation helps...
  44. R

    A eigenstate of addition of angular momenta

    Homework Statement l~m\rangle l=l_1+l_2 l_1=2,l_2=1 Find eigenstates(ofL_z) |2~0\rangle Homework Equations The Attempt at a Solution |l=3~m=3\rangle=|l_1=2~m_1=2\rangle|l_2=1~m_2=1 \rangle. I do L_-=L_{1-}+L_{2-} 3times. So I get |3~0\rangle= (omit) Then How can I find...
  45. C

    Vector Addition: Finding Displacement

    I am having a lot of trouble with my homework. If anyone could help me, it would be much appreciated. The Smith's go on vacation. They travel 16.0 km north/west; then turn 27 degrees to the left and go 135 km; then 294 km south/west. What is their displacement from home? So I found the X...
  46. S

    How Does Phasor Addition Simplify Trigonometric Expressions?

    Homework Statement Define x(t)=5cos(wt)+5cos(wt+120)+5cos(wt-120) simplify x(t) into the standard sinusoidal form:x(t)= A cos(wt+phase).Use phasors to do the algebra.Homework Equations The Attempt at a Solution i know it needs to use phasor addition rule. First,i represent x1(t),x2(t),x3(t) by...
  47. M

    Subjects in addition to Physics requirements; scheduling.

    (If there is confusion about course content, see links at bottom of post for course descriptions.) So looking ahead to the next 3 semesters, I can plainly see what classes I NEED to take for Physics.. but they leave room for courses in other disciplines -- for example Engineering, Computer...
  48. E

    Binary Addition Homework: 010110000000000 & More

    Homework Statement 010110000000000 011001000000000 001100010000000 100100001000000 110100000000100 111100000000001 + ------------------- Homework Equations The Attempt at a Solution The answer I get is 1010111011000101 but I have used MATLAB and the first four digits are...
  49. D

    How Fast is C Moving Relative to B?

    Homework Statement relative to A, B is moving towards A at a speed of 0.4c. Farther out C is moving towards A at a speed of 0.5c. all motion is along the x-axis how fast is C moving relative to B? Homework Equations U = (U' + V) / 1+ VU'/c^2 The Attempt at a Solution...
  50. T

    Equivalence relations and addition

    Homework Statement prove that if a~a' then a+b ~ a' + b Homework Equations The Attempt at a Solution I can prove that if a=a' then a+b = a' + b but how can I apply this to any equivalence relation
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