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. A

    How to Find Vector Components Along an Axis

    1. Vector A has a magnitude of 3 m and makes an angle of 10o with the positive x axis. Vector B also has a magnitude of 10 m and is directed along the negative x axis. Enter your answers in distance then angle(in degrees). Find A + B Find A - B 2. R = sqrroot(Cx^2+Cy^2) Cx = Ax+Bx Cy...
  2. S

    Buffer Question - With addition of OH-

    Homework Statement You add 100 mL of 1 M H3A and 4 mL of 5 M NaOH all in 896mL water Ka=6.309x10^-10 What is pH of solution made? H3A+H2O---->H2A-+H3O+ Homework Equations ka=[h2a][H+]/[H3A] The Attempt at a Solution Concentrations initially: [H3A]=100mL * 1 M / (896+4+100) mL = 0.1 M H3A...
  3. G01

    Derive Expression for Total Spin State |1,0> w/ 4 Spin-1/2 Particles

    Hi Guys, this is from my grad quantum class. I'm pretty stuck and need some help: Homework Statement Given four spin-1/2 particles, derive an expression for the total spin state |S,m⟩ ≡ |1,0⟩ in terms of the the four bases |+⟩i , |−⟩i ; i = 1,2,3,4 Homework Equations Clebsch Gordon...
  4. C

    Vector Addition: Calculating Bird's Speed in Southerly Direction

    A bird can manage 50 KmHr-1 in still air. There is a wind blowing eastward at 30kmhr-1, the bird wishes to travel south. The resultant speed the bird carries in the southerly direction is? For equations i just used vector addition, and pythagorous (A2+B2=C2) The first time i...
  5. L

    Finding the Angle and Magnitude of a Resultant Force using Vector Addition

    1. If the resultant force acting on the bracket is to be 790N directed along the positive x axis, determine the magnitude of F 2. Basically I got the components of the two vectors above and below F summed them up. I got THE RESULTANT X-component: 600cos45+325(5/13)+790cos(theta)...
  6. T

    Addition of AC current and compound angle theory

    Homework Statement two alternating currents I1 and I2 flow into a circuit node,the output current I is given by adding I1 and I 2. find I and t, when I1 and I2 are as follows Homework Equations I1=5sin(50t +Pi/3) I2=6cos50t The Attempt at a Solution...
  7. S

    Vector Addition: Finding Resultant and Direction - Easy Homework Solution

    Homework Statement I have three vectors and I need to find the resultant of the three vectors and direction. Homework Equations *All angles are with the horizontal Vector 1 = 18 at an angle of 40 degrees (First Quadrant) Vector 2 = 10 at an angle of 72 degrees (Second Quandrant)...
  8. B

    Distance formula and addition of meters per s

    Hello guys. I have issues understanding a rather simple physics concept and I hope you can help me out. I've tried asking help from several people, but nobody was able to isolate the problem. For constant acceleration, it is said that d=(Vi+Vf)/2*t. d being distance, Vi is initial velocity...
  9. 3

    Is R under addition isomorphic to R\{0} under multiplication?

    Homework Statement Is \mathbb{R} under addition isomorphic to \mathbb{R}\backslash{0} under multiplication? The Attempt at a Solution It is true that \mathbb{R} under addition is isomorphic to \mathbb{R}_{>0} under multiplication, by using the bijection \phi ...
  10. F

    Closedness of Matrices Under Addition & Multiplication

    Homework Statement 1. Show that the set M of symetric matrices is closed under addition and scalar multiplication. 2. Show that the set W diagonal matrices is not closed under addition and scalar multiplication. 3. Show that the set W of matrices such that transpose(A) = -A is closed under...
  11. L

    Proving Z is a Ring with Addition and Subtraction

    Homework Statement Prove that Z with the following addition and subtraction is a ring. Homework Equations a\oplusb = a + b - 1 and a\odotb = ab - (a + b) + 2 The Attempt at a Solution I proved all the axioms for addition. I'm stuck on the multiplication part...
  12. D

    Dealing with addition of cosntant to wave equation? Spherical Harmonics

    Homework Statement I am trying to calculate the angular momenta for \psi(x,y,z) = A(ar^2 + bz^2) A is given as a constant. Homework Equations The Attempt at a Solution I know that z=r\sqrt{4\pi/3} * Y_0^1 What I have so far is:- \psi(x,y,z) = r^2Aa +...
  13. H

    Equivalance classes and integer addition

    Homework Statement Prove: If a and b are in N the [(1,1+a)] + [(1,1+b)] = [(1,1+a+b)] Homework Equations Definition: We define + over Z as follows: if [(a,b)] and [(c,d)] are any two equivalence classes, we define [(a,b)] + [(c,d)] = [(a+c,b+d)]. The Attempt at a Solution So...
  14. D

    Vector addition analytical & component method

    hello everyone I am just new here i need help with my homework here's the problem A cross skier skis 7.40 km in the direction 45° east of south then 2.80 km in the direction 30.0° north of east and finally 5.20 km in the direction 22.0° west of north . Find the resultant vector using...
  15. A

    How to Calculate Net Force in Vector Addition with Given Forces and Angles?

    How do you find the net force in vector addition, for example if I have F1 = 64 N @ 30 degrees and F2 = 45 N @ 45 degrees and F3 = 78 N @ 330 degrees how would I go about finding the net force?
  16. T

    Counting and probablity addition rule?

    A calculator has an eight -digit display and a decimal point that is located at the extreme right of the number displayed, at the extreme left or between any pair of digits. The calculator can also display a minus sign at the etreme left of the number. How many distinct numbers can the...
  17. E

    Special Relativity Velocity Addition: Vector or Axis?

    I know how to add speed in special relativity. v=\frac{u+v'}{1-\frac{uv'}{c^2}} Is this a vector thus velocity? Or does this only apply to objects traveling on the same axis? Judging from the way it's derived, I really think that it only applies to objects on the same axis. What if I want...
  18. H

    Proving the Addition of Dedekind Cuts

    Homework Statement Show that if \alpha and \beta are Dedekind cuts then so is \alpha + \beta={r1+r2: r1 \epsilon \alpha and r2\epsilon\beta Homework Equations The Attempt at a Solution If a dedekind cut is a cut whereby the sets on the left side of the cut and the right side of...
  19. P

    Vector resolution and vector addition

    Homework Statement We were given six homework assignments for lab. We were required to find the force and angle through three given experiments. 1. Experimental using a force table 2. Graphically using head to tail, etc 3. Analytical using basic means to find the answers...
  20. P

    Relativistic Addition of Velocities

    Homework Statement A rocket is traveling at speed V along the x-axis of frame S. It emits a signal (for example, a pulse of light) that travels with speed c along the y prime axis of the rocket's rest frame S prime. What is the speed of the signal as measured in S? Homework Equations...
  21. L

    Laurent series: addition and multiplication of series

    Find the Laurent Series around z=0 for f(z) = \frac{{2{z^2}}}{{2{z^2} - 5z + 2}} + \sin (\frac{3}{{{z^2}}}), so that the series absolutely converges in z = -i The Attempt at a Solution The singularities of f are z = 0, z = 1/2 and z=2. The Laurent series will converge absolutely in z = -i...
  22. L

    Can addition formula be applied to more than 2 sums?

    Homework Statement Not an actual problem, but to help solve my homework, would cos(A+B+C)= CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny) I was unsure if this can be applied to multiple digits or only 2. I know I could plug in numbers to test, but I was wondering about...
  23. N

    Java Java int addition - the long way

    Hi guys, I'm trying to figure out a way to split up integers so I can do addition the old school way in Java. E.g.: 1234 1234 +_____ 2468 So you know start at the 4's and then add them up and move left etc. Does anyone have any ideas on how I access the different digits of...
  24. D

    What is the Concentration of Vitamin A in Serum Using HPLC?

    Homework Statement The concentration of retinol (vitamin A) in serum was determined by HPLC with UV absorbance detection. A 1.00 mL sample of serum was placed in a 10 mL test tube. To precipitate the proteins, 800.0 microL of ethanol was added, and the test tube was agitated. Next, a 2.00 mL...
  25. V

    Vector Addition Help: Finding the Resultant Vector using the Component Method

    EDIT: ****Nevermind, I just mis-typed everything into my calculator. I had to put my X and Y values in parenthesis - ie sqrt((29.47)^2 + (-5.32)^2)************** I *think* I am doing this right, but I can never get the right answer. Does anybody notice what is going wrong? The correct...
  26. K

    Relativity_velocity addition and doppler effect

    Homework Statement The Enterorise NCC1701 is cruising 0.6c above the moon of Eridani when it spots a Klingon warbird sunwards. i. It fires a proton torpedo at speed 0.75c relative to the ship at the Klingon warbird. Assuming the proton torpedo does not accelerate, at what velocity must the...
  27. C

    Addition of Families of Intervals Question

    Homework Statement Let A= {[-2,5],[1/2,2]} and B={[1,7],][1/4,3]}. Calculate the family A+B.Homework Equations Given F and G families of intervals, F+G is the family {I+J \left| I\inF, J\inG}The Attempt at a Solution I don't understand how to calculate A+B from this equation. How do you know...
  28. B

    How Fast Are Proton and Antiproton Moving Towards Each Other?

    Homework Statement A proton and an antiproton are moving toward each other in a head-on collision. If each has a speed of 0.8c with respect to the collision point, how fast are they moving with respect to each other? Homework Equations Ux = [U'x + V] / [1 + (v/c^2) Ux'] The...
  29. A

    Addition of vectors and direction

    Homework Statement A vector A has a magnitude of 56.0 m and points in a direction 20.0° below the positive x axis. A second vector, B, has a magnitude of 70.0 m and points in a direction 45.0° above the positive x axis. Using the component method of vector addition, find the magnitude and...
  30. T

    Vector addition using graphical method

    Hello, How do I use the graphical method of vector addition to determine the magnitude and direction of the resultant displacement? Just the steps on how to determine displacement vectors??
  31. C

    Vector addition using components

    Homework Statement You will be hiking to a lake with some of your friends. the map says you will travel 1.6 mi north then 2.2 mi in a direction 35 degrees east of north, then finally 1.1 mi in a direction 15 degrees north of east. how far will you be from where you started and what direction...
  32. M

    Get Applied Math BS in addition to Physics? (Goal=Medical Physics)

    I was thinking about postponing my graduation one year to get a BS in Applied Mathematics in addition to my Physics BS. My goal is to get into a top Medical Physics program. I am currently a member of a Medical Physics research group here at my school and have impressed my advisor. He thinks...
  33. K

    Velocity Addition: Lead Photon Movement?

    still don`t have an answer i can understand. If a moving emitter moves at .99 c, does the lead photon move away from the emitter such that it is c x time away from the emitter at any point in time? (not asking about the original position of the emitter when it emitted)
  34. D

    How to solve vector addition problems for physics?

    1. For the vectors given in Fig. 3-32 (|A| = 64.0 and θ = 51.0°), determine the following. Find the magnitude and direction for each of the following : 1) A-B+C 2) A+B-C 3) C-A-B. heres a diagram with it: 2. The graph above should help, but I'm stuck on what to do 3. I basically...
  35. S

    Signal Addition: Beginner FAQs | Learn About Signal Sum

    I am just a beginner in Signals and systems... In signal addition when we add two signals for example u(t) and u(-t), we are supposed to just add the values of both the signals at each and every point to get the sum,right? so in the case of u(t)+u(-t), what will be the sum value at t=0? Is it...
  36. D

    Checking commutativity property with addition table

    I saw the technique of using a mathematical system called the "Four minute clock". Basically, the clock has 4 numbers, 0, 1, 2 and 3, and only one hand. We can make a summation table which will look like the image attached. According to the text, if there is symmetry (reflection) across the...
  37. O

    Does the presence of B change the velocity of C with respect to A?

    Let's say there are two observers A and C. C is moving .5c with respect to A. If we introduce a third observer which we will call B and B is moving at .2c with respect to A and is moving in the same direction as C and is inbetween A and C, and we now apply the velocity addition formula we get...
  38. S

    Proving cis(x1 - x2) - cis(x2 - x1) = 2cos(x1 - x2)

    Homework Statement Prove that cis(x1 - x2) - cis(x2 - x1) = 2cos(x1 - x2) The Attempt at a Solution Cis is a sin-and-cos summation. Shortly, cisx = cosx + isinx How can you prove the statement?
  39. R

    Multiplication and addition principle for count possibilities?/

    multiplication and addition principle for count possibilities??/ we toss a fair coin 5 times and recored the sequence of head and tails obtained.how may sequences are possible that start with head OR end with head.? so what i did was using addition theorm i divided this complex process...
  40. C

    Relativistic Addition of Electron Velocities

    Homework Statement An electron moves to the right in a laboratory accelerator with a speed of 0.822c. A second electron in a different accelerator moves to the left with a speed of 0.424c relative to the first electron. Calculate the speed of the second electron (in c) relative to the lab. Do...
  41. V

    Solubility Problem - Involves Addition of Another Ion

    Homework Statement How many moles of solid sodium fluoride should be added to 1.0 L of a saturated solution of barium fluoride, BaF2, at 25OC to raise the fluoride concentration to 3.0 x 10-2 mol/L? The solubility product constant for BaF2 is Ksp = 1.7 x 10-6 at 25OC. The Attempt at a...
  42. M

    How to Express Trigonometric Functions in the Form x = Rsin(t + ø)?

    Homework Statement 1, Express x = 3sin3t + 5cos3t in the form of x=Rsin(3t + ø) 2, Express x = 2sin(0.5t + 3) + 3cos(0.5t + 1) in the form x = Rsin(0.5t + ø) All working must be done in radians. Homework Equations Sine and Cosine Addition Formulae sin(A + B) = sinAcosB +...
  43. C

    A question on velocity addition

    Consider frame S1 and another frame S2 moving with a velocity v with respect to S1 along +X direction. Consider a photon comes in -X direction. Velocity of photon in S1 is c.I would like to find the velocity of light in S2 from S1 without forgetting length contraction and time dilation as...
  44. Z

    Cancellation property of addition of natural numbers

    I have to prove that for all k,m,n \in N that if m+k = n+k, then m=n. The problem mentions that I must prove this by induction. I did the base case k = 0: If m+0 = n+0, by identity m=n. Then I attempt to show that m+1 = n+1 implies m=n, but I am stuck, I don't see how induction can be...
  45. Fredrik

    Tell me what I'm doing wrong (velocity addition in 3+1 dimensions)

    A 3+1-dimensional Lorentz transformation can be written as \Lambda=\gamma\begin{pmatrix}1 & -v^T\beta \\ -v & \beta\end{pmatrix} where v is a 3×1 matrix representing the velocity difference, \gamma=1/\sqrt{1-v^2}, and \beta is a 3×3 matrix that's orthogonal when v=0. When \beta=I, \Lambda is...
  46. W

    Find Angle Between Vectors A & B: 105.27

    Homework Statement Find the angle between the following vectors? A = -2.00i^ + 6.00j^ and B = 2.00i^ - 3.00j^ (the ^ means 'i hat') Homework Equations Theta = tan^-1 = (opposite/adjacent) The Attempt at a Solution i said for the first part of the component that theta(A)...
  47. B

    Vector spaces, closed under addition

    Homework Statement Let S={A (element) M2(R) : det(A) = 0} (b) Give an explicit example illustrating that S is not closed under matrix addition.Homework Equations The Attempt at a Solution 1) I think that the problem is saying S is a set of 2x2 matrices, whose determinant is zero? 2) I'm...
  48. Mentallic

    Can Pi minus e ever equal a rational number?

    Can such irrationals like \sqrt{2}, \pi, e ever be added/subtracted to another irrational to give a rational result? This would have to exclude such occurences like: \sqrt{2}+(1-\sqrt{2}) and less obvious irrationals that - for their irrational parts - can be expressed as the negative of the...
  49. Math Is Hard

    Addition to Philosophy Forum guidelines

    Hi everyone, I just wanted to let you know about this new addition the Philosophy Forum guidelines. https://www.physicsforums.com/showthread.php?t=47294 The intent is not to become obnoxiously strict "grammar police" here, but to create standards that will facilitate communication. We have...
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