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. R

    Deriving addition of sines from Euler's formula

    Deriving addition of sines from Euler's formula (edit: please ignore) Homework Statement I'd like to derive the value of sin(2πkt + θ) so that I can convince myself that the Fourier sum in terms of sines and cosines works. I found the derivation on Wolfram by using the full Euler's formula...
  2. B

    2D Vectors - Addition and Subtraction of Successive Displacement Vectors

    The figure shows the successive displacements of an aircraft flying a search pattern. The initial position of the aircraft is P and the final position is P'. What is the net displacement (magnitude and direction) between P and P'? My attempt: So, my understanding is that the net...
  3. P

    Vector addition word problem question

    I solved a word problem correctly...But I'm a little confused about what my answer means, I guess I'm having trouble understanding how they got the meaning of the numbers. My question is about step (b). Problem: The velocity of an aircraft is 200 km/hr due west. A northwest wind of 50 km/hr is...
  4. M

    How can we add Angular Momenta in Quantum Mechanics?

    Hey! While I was reading some book in Quantum Mechanics, I ran across the following, and couldn't know how can this be true or actually how was it assumed. How by adding equation (7.91)and (7.92), we get (7.110), see attachment.
  5. T

    The tension between addition and multiplication - the basis for all mathematics?

    Throughout mathematics, we see the appearance of pi and e, they are integral to every part of mathematics. could this be because the reason all or at least most mathematical problems arise because of the tension between multiplication and addition (pi and e) itself?. certainly the deepest...
  6. H

    Proving Subspace Addition: LHS vs RHS

    Homework Statement Let L,M,N be subspaces of a vector space V Prove that (L \cap M) + (L \cap N) \subseteq L \cap (M + N) Give an example of subspaces L,M,N of \mathbb{R}^2 where (L \cap M) + (L \cap N) \neq L \cap (M + N) Homework Equations The Attempt at a Solution...
  7. D

    Why am I getting this relativity velocity addition problem wrong?

    Homework Statement A spacecraft S2 is capable of firing a missile which can travel 0.98c. S2 is escaping from S1 at a speed of 0.95c when it fires a missile towards S1. part A) According to the pilot of S2, what speed does the missile approach S1? Part B) according to pilot of S1, what...
  8. J

    Addition of Angular Momenta, problem with notation

    Homework Statement The electron in a hydrogen atom is described by the following superposition of two states: |\psi> = \frac{1}{\sqrt{2}}(|n=2,l=1,m=0,s_z= +1/2> + |n=2,l=0,m=0,s_z= +1/2>) (b) Let J = L + S be the total angular momentum. Express state \psi in basis |n, l, J, J_z>...
  9. O

    Phasor Addition Techniques: Adding Frequencies, Amplitudes & Phases

    Hello, I was wondering about the adition of phasors with different amplitude, frequency and phase. Wikipedia supplied the technique of adding phasors with the same frequency but different amplitude and phase (http://en.wikipedia.org/wiki/Phasor#Addition). When it comes to adding phasors...
  10. S

    Having a hard time thinking about quantum mechanical vector addition.

    If a neutron in a nucleus is in a 1p state, before splitting this up into separate j-state (due to spin-orbit effect) this neutron has 6 possible states. l = 1 m_l = 1, 0 or -1 m_s = 1/2 or -1/2Splitting this into j-states corresponding to l+s and l-s, as expected there are 6 states. j = 3/2...
  11. mnb96

    Question on isomorphism between addition and multiplication

    Hello, I want to find a family of functions \phi:\mathbb{R} \rightarrow \mathbb{C} that have the property: \phi(x+y)=\phi(x)\phi(y) where x,y\in \mathbb{R}. I know that any exponential function of the kind \phi(x)=a^x with a\in\mathbb{C} will satisfy this property. Is this the only choice...
  12. R

    Velocity Addition in Special Relativity

    Hi All, Pardon me if this question looks so silly. Trying to understand velocity addition in special relativity. Say velocity components as measured in stationary frame of reference S are u, v, w in x, y, Z directions respectively and those in moving frame S' are u', v', w' in x', y', z'...
  13. X

    Trigonometry- addition and factor forumla

    Homework Statement If tan(A+B) = 3 and tan(A-B) = 2, find tan2A and tan2B Homework Equations tan (A - B) = (tan A - tan B)/(1 + (tan A)(tan B) and similar sort of one for tan(A+B) The Attempt at a Solution i did some calculation and got tanA= (1-2tanB)/5tanB after which there...
  14. A

    Entropy: Heat addition to surrounding.

    If 12007 kJ of heat is lost to the surroundings with an ambient temperature of 25 degrees centigrade during a cooling process, and the ambient temperature of the surroundings is unaffected by the heat addition, what is the entropy change of the surroundings? If Δs=∫δQ/T, then Δs=ΔQ/T=12007...
  15. L

    The meaning of the addition of the spin generator to the Lorentz generators

    When constructing the Lie algebra of the Lorentz Transformation, the references usually start with an infinitesimal proper-orthochronous transformation, and then find the infinitesimal generators. Let's call the set of these generators L. after finding L, the references usually compute the...
  16. L

    Vector Addition Help: Solving P = M + N

    Homework Statement Alright so i need to add these using vector addition i suppose. P = M + N P = 1.8304 kgxm/s (S 6° W) + 3.2864 kgxm/s (S 42° W) The Attempt at a Solution This is my half attempt: http://s1176.beta.photobucket.com/user/LolaGoesLala/media/ggfgf.jpg.html But i don't...
  17. J

    Relativist Addition of Velocities

    Homework Statement Fix an inertial reference frame and consider a particle moving with velocity \mathbf{u} in this frame. Let \mathbf{u'} denote the velocity of the particle as measured in an inertial frame moving at velocity \mathbf{v} with respect to the original frame. Show the following...
  18. J

    Addition of angular momenta, rotation operators

    Hey, I have a question regarding the invariance of a 'mixed' Casimir operator under rotation, By 'mixed' Casimir operator I refer to: \vec{J}_1\cdot \vec{J}_2 Where J1 and J2 are two independent angular momenta. I want to show that this 'mixed' Casimir operator is invariant under...
  19. Drakkith

    New Addition to the Family: Celebrating Baby Girl's Birth!

    Uh oh, I'm an uncle again! Healthy baby girl born to my sister today! Anyone else had any new additions to the family recently? Are there any traditions in your family related to births?
  20. O

    The picture in the addition, you see one integral equation and I have

    The picture in the addition, you see one integral equation and I have moved forward to solve it but when I tried to use patial integrant ( uv-∫v.du) I couldn't go further, Is there anyone to help me solving that equation.Actually, I stuck while putting the boundries (from 0 to ∞ ) because it...
  21. H

    Effect of electron addition to various properties of atom

    Homework Statement Describe what happens to the ionization energy, electronegativity and atomic radius as electrons occupy the next sub level. Homework Equations The Attempt at a Solution My (probably incorrect) answers: Ionization Energy: As electrons occupy the next sub level...
  22. J

    Proving that a set is a Vector Space - addition is defined very oddly

    Homework Statement Let V = {0,1} with addition defined modulo 2 (i.e. the remainder upon division by 2), and scalar multiplication given by ku = u^k for all k in the real numbers and u in V. Is the set V a vector space? Homework Equations The 10 axioms! The Attempt at a Solution I...
  23. M

    Subtraction using 2's complement addition question

    The problem states: "What Intel x86 instructions would you use to accomplish subtraction using 2’s complement addition? This instruction set has a SUB instruction, but don’t use that; write your own 2’s complement routine instead". Then the book states the answer: MOV 51, EDX // copy...
  24. D

    How to derive the velocity addition formula

    Homework Statement Derive the formula v= (v'+u)/(1+v'u/c^2) the velcoty addition formula using the below formulas? Homework Equations 1. vt1=L+ut1 2. (proper time)=(proper length)/v'+(proper length)/c 3. ct2=L-ut2 4. (dilated time)= (proper time)/(sqrt(1-v^2/c^2)) 5. L=(proper...
  25. A

    How do I calculate the correction value for a 6-bit number in binary addition?

    In BCD addition when the number exceed 9 we add 6 as the correction value. Although I tried all the cases and saw tthat 6 was indeed the asnwer, how do I prove that? Suppose that instead of BCD I had a 6-bit number, what would be the correction value for that coding?
  26. N

    Why is my Angular Momentum Homework Solution Incorrect?

    Homework Statement So I'm told I can't do it this way but I was wondering if anyone could clarify as to why? We're given |J=\frac{1}{2},M = \frac{1}{2}\!> where j_1 = 1 \, and \, j_2 = \frac{1}{2} Homework Equations The Attempt at a Solution So this can be composed as a linear...
  27. G

    Can Basic Addition Reach Higher Level Mathematics? A Mathematician's Perspective

    Hello, mathematicians, I have a very simple question. Well its simple to state. Can you arrive at all the higher level mathematics with plain addition? Here's an example of what I mean. Can you calculate things like trigonometry and logarithms with just addition? I ask this question because...
  28. O

    MHB On the Implication of Addition Axioms

    Hello everyone! I was trying to prove the propositions that follow the addition axioms as a revision, I got a different proof for the following proposition: If $x+y=x+z$ then $y=z$ My proof was the following: $x+y=x+z$, $(-x)+x+y=(-x)+x+z$, $0+y=0+z$, $y=z$ Rudin however, in his book...
  29. S

    Given a Vector addition and subtraction, how to find the Vector.

    Homework Statement Given the following Vectors: A+B= x1i + y1j and A-B= x2i + y2j what is A? and what is B? The Attempt at a Solution I wasn't really sure how to go about this problem. I tried setting one side to A and pluging it into the other eqn A.. however that made no sense to me.
  30. A

    Basic special relativity addition of velocities problem

    "An electron moves to the right with a speed of 0.90c relative to the laboratory frame. A proton moves to the right with a speed of 0.70c relative to the electron. Find the speed of the proton relative to the laboratory frame." u' = (u-v)/(1-(uv/c2)) where u will be velocity of electron...
  31. Ryuzaki

    Triangle Inequality and the Triangle Law of Vector Addition

    The triangle inequality states that, the sum of any two sides of a triangle must be greater than the third side of the triangle. But the triangle law of vector addition states that if we can represent two vectors as the two sides of a triangle in one order ,the third side of the triangle...
  32. D

    Do abstract things and spiritual things exist in addition to physical things?

    Do abstract things (e.g. numbers) and spiritual things exist in addition to physical things? Or is everything physical? I'd say that mathematics is certainly real, yet not physical. It wasn't just invented by humans.
  33. R

    Addition of orbital angular momentum in valence 4f^2 electronic configuration

    I am trying to self-learn quantum mechanics pertaining to Lanthanide ions. For a given set of J and MJ quantum numbers in a valence 4f^2 electronic configuration, J=0,2,4,6 and MJ=0,6,-6. The |J,MJ> basis functions are |0,0>, |2,0>, |4,0>, 1/2[|6,6>+|6,-6>]+sqrt(1/2)|6,0>, and...
  34. J

    Can concentrated hot sulfuric acid directly react with alkenes?

    Alkenes react with concentrated sulphuric acid in the cold to produce alkyl hydrogensulphates. If the alkyl hydrogensulphate is diluted with water and heated, alcohol is obtained My question: Can alkenes react with hot conc h2so4 directly?Any reaction between them? What are the products...
  35. C

    Electrons - Relativistic velocity addition

    electrons -- Relativistic velocity addition... Homework Statement an observer measures the velocity of two electrons, finding one with a speed c/2 in the x direction and the other c/2 in the y direction. what is the relative speed of the two electrons. Homework Equations The...
  36. C

    Proving Closure of Set of Operators w/ Property P Under Addition

    Could you please give me a hint on how to show that a set of operators with a property P is closed under addition? In other words, how one could prove that a sum of any two operators from the set still possesses this property P. The set is assumed to be infinite. Any references, comments...
  37. M

    Decomposition of Vector Addition to lead to unique solution

    I have a puzzling question that a gentleman discussed and have differnt view on the problem, the probelm goes as follows: What is know is the Resultant of a Vector Addition, the goal is to find the two vectors from which the resultant came from. The other piece of information that is know is...
  38. M

    How to draw a phasor addition on AC circuit?

    How to draw a phasor ? Homework Statement Two alternating currents are applied out of phase with each other. One is 4 volts and the other is 3 volts 27° out of phase. These can be written as (4, 0°) and (3, 27°) Homework Equations a)draw both phasors b)draw the combined phasor...
  39. G

    Vector Addition Homework: Multiplying Vectors & Gaussian Elimination

    Homework Statement Homework Equations The Attempt at a Solution Do you see how 1 1 1 changes to 3 3 3. i know why gaussian elimination you can change any vector by multiplying it by anything you want. but for some reason i have difficulty believing that you're allowed to do that here. is...
  40. S

    Where does the energy go when two out of phase signals are added?

    I have a solar energy system at my home. It basically uses an inverter that converts DC from the solar panels to AC that is phase-locked to the service from our electric company, then adds the two together to feed the home. There are two meters – one to measure the energy produced from solar...
  41. V

    Definition of vector addition, Cartesian product?

    I'm reading through a multivariable calculus book and it starts off with some linear algebra. It defines vector addition as V \times V \rightarrow V. My text describes V as a set and describes the above process as a mapping. I believe the \times may represent a Cartesian product. Could someone...
  42. O

    Summing sines/cosines (Harmonic Addition Theorem)

    I have a mathematical model which, in part, does a calculation based on the location of certain points on a unit circle. I am just working in 2d so for some arbitrary values of a,b,c,d,e,f In the case of the unit circle equally divided so that I have three points on the unit circle (120°...
  43. A

    Understanding the Addition Theorem for Modular Operations

    Hello all, I was wondering if someone can explain to me a step in a proof given to me by my professor in regards to a modular operation theorem. Addition theorem: Given three integers x, y, d (d > 0), (x+y)%d = (x%d + y%d) %d Proof: Let x = q(1)d + r(1) and y = q(2)d + r(2). We have...
  44. C

    Simple Vector Addition Question

    I'm not sure if this the correct area but Ill go ahead anyways. I have three points (A, B, and C) in 3D space that form a triangle. All three points have the (x,y,z) coordinates defined. Using the dot product I have solved for the angle θ (or in other notation the angle ABC) of the...
  45. P

    Adding Vectors: Using Angles and Formulas | Vector Addition Explained

    To add two vectors, a\rightarrow and b\rightarrow we use the formula \sqrt{}a2+b2+2abcosθ where θ is the smallest angle between vectors a and b. Is there any way I can use the bigger angle to calculate the sum ? It's not a homework, just a question from my intution. I have attached a pic...
  46. P

    Rational numbers that form a group under addition

    Rational numbers form a group under addition. However, a sequence of rational numbers converges to irrational number. Presumably, group theory does not allow adding an infinite number of rational numbers. This is not indicated in the textbook definition of a group. I might be looking in vain...
  47. A

    Vector addition and motion diagram

    Mastering physics Knight. 2nd edition. A figure shows two dots of a motion diagram and vector \vec{V}_{1} Copy this figure and add vector \vec{V}_{2} and dot 3 if the accelration vector \vec{a} at dot 2 (a) points up and (b) points down. \vec{V}_{1} is a vertical vector pointing upward with...
  48. V

    Special relativity - A problem on velocity addition (several increments)

    Homework Statement A spaceship, at rest in a certain reference frame S, is given a speed increment of 0.50c. Relative to its new rest frame, it is then given a further 0.50c increment. This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many...
  49. E

    Addition of spin angular momenta

    Hi I am working my way through Griffith's Introduction To Quantum Mechanics and I have got to the section on addition of spin angular momenta. I'll copy and paste the bit I'm struggling with, as it's easier than paraphrasing: http://img714.imageshack.us/img714/2783/80183858.png...
  50. L

    Conjugate Addition and Ether Formation

    Homework Statement http://i43.tinypic.com/nxvw41.jpg Ok here it is molecule B. http://i39.tinypic.com/333aaro.jpg Ok and here it is problem nr. 8, second molecule. Homework Equations No equations needed. The Attempt at a Solution 1) So why is it that we do not add any...
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