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. X

    I Integration over something with addition in denominator

    Hi, I'm struggling to figure out how to do integration with forms such as: ∫ x/(x+1) dx ∫ x/(x+1)^2 dx ∫(b-x)^2/(b-a) dx This last one especially is giving me a strange issue, where if I plug it into wolfram: https://www.wolframalpha.com/input/?i=integrate+(b+-+x)%5E2+%2F(b-a)++dx It shows...
  2. M

    Standard addition concentration positive

    I am computing limit of detection of zinc of an electrolyte. Using standard additions method, I have obtained positive x intercepts for 6/8 samples all very close to zero. Positive x-intercepts imply final concentration values to be negative. if x-intercept taken to be zero, the concentration...
  3. I

    I Velocity Addition & Relativity of Simultaneity

    I have some issues understanding the following thought experiment: Suppose you are standing still, and two balls are moving towards you from opposite direction. From your own reference frame, Ball A is ##10^5## m away from you, moving towards you from the left with speed ##0.8c##, and Ball B is...
  4. M

    Understanding Sinusoidal Waves: Exploring Phase, Wavelength, and Amplitude

    Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad), A. with x in meters and t in seconds. What is the wavelength λ of the two waves? B. What is the phase difference between...
  5. O

    I Velocity Addition Example: Morin's Confusing Use of Equation

    Ok, so here's another example Morin did in his book: Ok, so the thing that confuses me is when he used the velocity addition equation: Note:4c/5 and 3c/5 are their speeds relative to the ground. Where v2 is the velocity of the S' frame, and v1 is the velocity of the object moving in the...
  6. L

    I How to define addition and multiplication using Peano's axioms?

    How can one define addition using peanos axioms? Number, successor, zero are terms which we presume to know the meaning of. We then use five propositions: 1. 0 is a number. 2. Every number has a successor. 3. 0 is not the successor of any number. 4. Any proeprty common to zero and its...
  7. Toby_phys

    Addition of masses in relativistic collision

    Really basic question: a particle, moving at speed u (u is fast enough for relativistic effects) with rest mass m0 collides with a stationary particle with rest mass m0. They coalesce to form a new particle of mass M (observer fame, not rest mass M) and move at speed v. find v in terms of y (y...
  8. shina

    What is the formula for adding a sequence of consecutive numbers?

    Homework Statement Homework EquationsThe Attempt at a Solution hey hello every one I want to ask a question that is add 1+2+3+4.....10000000. I think its very easy. for example let us add first 5 numbers 1+2+3+4+5 now we can find a pattern that adding first and last digit will be always same...
  9. ManicPIxie

    Relativistic Addition of Velocities

    This question comes from a previous years exam as practice for my upcoming. Homework Statement Two spaceships are launched from Earth, going in opposite directions. Eventually, both spaceships have a velocity of 0.75c (where c is the speed of light), each in their respective directions. A...
  10. T

    Why there isn't any unimolecular addition reaction?

    In my textbook, i have read about unimolecular elimination and nucleophilic unimolecular substitution reaction of organic compounds. In those reactions, firstly one bond breaks automatically then as soon as a carbocation forms then a nucleophile attacks the carbocation to complete the reaction...
  11. M

    I Why does the author use the notation ##f_c(d)## instead of ##f(c,d)##?

    Hello everyone. I have read a proof but I have a question concerning the notation. To give some context, I will write down this proof as written in the book. Theorem: There is a unique binary operation ##+: \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}## that satisfies the following two...
  12. A

    I Simple physical example for addition of angular momentum?

    I've been asked to replace a professor for a couple of classes in an undergraduate quantum mechanic course. I have to present some topics on angular momentum, including the addition of angular momentum. I have no problem with the general theory and can present it just fine. But I would like to...
  13. Marcin H

    Binary Addition - 2's Compliment Representation

    Homework Statement Homework Equations Binary Arithmetic The Attempt at a Solution Is this the right way to do these problems? If I see a binary 1 at the beginning of the binary number do I just do the 2's compliment of that and add them? I am not too sure what it means by assume numbers...
  14. I

    Qualitative understanding of Maxwell's addition

    Can somebody please give me a qualitative understanding of how a moving electric field creates a magnetic field and vice versa per maxwells equations? Thanks!
  15. C

    Understanding Shear Force: Uniformly Varying Load in Region EF

    Homework Statement I'm having problem of the shear force at the uniformly varying load at region EF... Why the shear force isn't -26 +(-30*4/2) at E? but -26 +(-30*4/2) at F?Homework EquationsThe Attempt at a Solution as we can see the force at region F is 0. the force due to uniformly varying...
  16. Stephanus

    B Hubble flow and velocity addition

    Dear PF Forum, I've been wondering about this thing. The universe's radius is 46 gly. But a galaxy in 13.8 gly from us cannot be seen because it travels faster than the speed of light. So is there a galaxy in, say, 30 billions light years away from us? But before that, I'd like to know about...
  17. evinda

    MHB How is binary addition performed?

    Hello! (Wave) According to some notes of computability theory: Addition of binary numbers $$10011\\ +11111 \\ ------ \\ 110010$$ I haven't understood how they do the addition, since it holds that $1+1=0$... (Sweating) Could you explain it to me?
  18. CynicusRex

    B Mistake when explaining associativity of vector addition

    Does he make a mistake at 6:18? In case of associativity. When doing a+(b+c) he's just placing the tip of a to the tail of (b+c), but shouldn't he have added the tail of a to the tip of (b+c) ending in a different point? I understand vector addition is associative, but I think how he did it is...
  19. parshyaa

    I Parallelogram law of vector addition

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  20. parshyaa

    B The Addition of Two Vectors: A Visual Guide

    why addition of two vectors are represented by this diagram, why the sum of two vectors are between both the vectors. Does it takes the idea of hitting a ball , if we hit a ball to its left side it goes right side and when hitted to its right side it goes left side and when we hit...
  21. R

    B Polytropic process with heat addition

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  22. T

    Change in concentration in equilibrium caused by addition

    Homework Statement Cu2+ ions react with Fe2+ ions according to the following reaction. Cu2+ + 2Fe2+ --> Cu + 2Fe3+ At equilibrium, the concentration of Cu2+ ions is not changed by the addition of A) Cu2++B) Fe2+C) CuD) Fe3+. Homework EquationsThe Attempt at a Solution I chose A through...
  23. G

    I Velocity Addition: Physical Meaning of Non-Singularity at c?

    Hi. In the derivation of the relativistic formula for adding velocities, the Lorentz factor drops out. Mathematically, the formula works for inertial frames with relative velocity c and even gives an answer to Einstein's famous question about what happens if you drive at the speed of light and...
  24. C

    Momentum, vector addition question

    Homework Statement A car with a mass of 1400 kg is westbound at 50 km/h. It collides at an intersection with a northbound truck having a mass of 2000 kg and traveling at 40 km/h. What is the initial common velocity of the car and trucks after collision if it's an inelastic collision? Homework...
  25. Jameson

    MHB Adding Vectors with Head-to-Tail Addition: What Software to Use?

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  26. T

    B Number of concepts of Multiplication and Addition

    Hi,can someone exaplain me,why do we have a few concepts of multiplication,like repeated addition,scaling,grouping etc...but only one concept for addition that means to put something together and make it more or bigger I was solving in past,why multipliplication produce new unit and so on...but...
  27. R

    Show graphically/vector addition adding two waveforms

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  28. Amine_prince

    B Error in Vector Addition: U & V Perpendicular

    i have two unitary vectors in space U and V , U and V are perpendicular . W is a vector that verifies W ^ V = U - W . the following resolution is incorrect , i wan't to understand why : we use (o,U,V,(U^V)) . components of U (1,0,0) , V(0,1,0) , W(a,b,c) where a , b and c are real...
  29. P

    B Heard of Another Kind of "Rational" (Fraction) Addition?

    I ran across this years ago. It’s defined by the addition rule: a/b + c/d = (a+c)/(b+d) (Sounds crazy – until you think of x/y as meaning There’s a pile of x things on one side, and one of y things on the other.) Applying it in almost a Pascal's Triangle sort of way generates ... er, a...
  30. S

    Uniqueness of identity element of addition

    Homework Statement Here, V is a vector space. a) Show that identity element of addition is unique. b) If v, w and 0 belong to V and v + w = 0, then w = -v Homework EquationsThe Attempt at a Solution a) If u, 0', 0* belong to V, then u + 0' = u u + 0* = u Adding the additive inverse on both...
  31. henil

    Addition of Frequencies: Combining Same Phase, Different Amplitudes

    i want to add two frequencies having same phase but different amplitudes, in what manner i can proceed ?
  32. J

    How Do You Sum the Components of Vectors in Three Dimensions?

    Homework Statement [/B] Given the following vector components of vectors C and D: Cx = 8.10, Cy = -5.40, Cz = -7.90, Dx = 4.40, Dy = -2.50, Dz = 4.50, find the x, y, z components of their sum. Homework Equations No relevant equations that I know of...[/B] The Attempt at a Solution I am...
  33. D

    What Angle Should the Goose Fly to Head Directly Southward?

    Homework Statement Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is flying at 100 km/h relative to the air but a 38 km/h -km/h wind is blowing from west to east. At what...
  34. Odious Suspect

    Geometric proof cross product distributes over addition

    If the cross product in ℝ3 is defined as the area of the parallelogram determined by the constituent vectors joined at the tail, how does one go about proving this product to distribute over vector addition? I've attached a drawing showing cyan x yellow, cyan x magenta, and cyan x (magenta +...
  35. M

    Is There Enough Information to Solve the Relativistic Velocity Addition Problem?

    Homework Statement Two asteroids are approaching one another moving with the same speed speed as measured from a stationary observer on Europa. Their relative speed is 0.5c. Find the speed of one of asteroids relative to Europa. I understand how relativistic velocity addition works but am not...
  36. C

    Add Vectors: 55km South + 34km North

    Homework Statement Illustrate the addition of the following two vectors and calculate the resulting vector: 55km [South] + 34km [North]. Homework EquationsThe Attempt at a Solution [/B] The attempt at the solution is below. What is troubling me is the overlap of the vectors and how to draw...
  37. Cecil L Russell

    Reflexive Property vs Commutative Property of Addition?

    Self Teaching myself Machine Shop Math from book Technical Shop Math by Thomas Achatz. According to the examples given, a=a is a Reflexive Property while a+b=b+a is described as a Commutative Property of Addition. The quiz question is: Name the property illustrated in the example. a) x+1=x+1. My...
  38. Sirsh

    Complex Number Division and Addition

    Homework Statement This is not for a mathematics unit but is part of an electrical question I'm trying to solve but I cannot solve this equation. The complex numbers Zp and Zr are both real and imaginary, whereas Xm is purely imaginary. Homework Equations Zp = (Xm*Zr)/(Xm+Zr) Zp =...
  39. DiracPool

    Bob's Relativistic Velocity Addition: 0.9c for Alice & Charlie

    My name is Bob. I'm floating in deep space and I have these two powerful cannons that shoot my friends Alice and Charlie in opposite directions to me, one to the left and one to the right. I shoot each out at 0.9c. As I look to the left, I see that Alice is flying away from me at 0.9c. Then...
  40. J

    Help with Vector Addition Problem

    Homework Statement In photo: https://gyazo.com/6348b5ffe368852ee9868a2ba0dd7e38 Homework Equations In image The Attempt at a Solution In the boxes Where did I go wrong with the angle calculation? Thanks
  41. Blockade

    How do I know that I should do a vector addition for this?

    I don't need help finding the resultant of this example problem. What I do need help for is: What exactly from this prompt hinted that I must add all the vectors provided. I have read this many times through and I still didn't know what to do. How does adding the vectors help them find the...
  42. person_random_normal

    How Does Silica Gel or Alumina Accelerate HX Addition to Alkenes in CH2Cl2?

    Adding silica gel or alumina to the mixture of the alkene and HCl or HBr in CH2Cl2 increases the rate of addition dramatically but WHY ? and why is CH2Cl2 specifically used ?
  43. Mr Davis 97

    Why is vector addition defined the way it is?

    We all know that arithmetic addition arose not out of some axiomatic system, but out of the natural tendency to combine similar objects. I am satisfied with typical addition being loosely defined in this way. But when it comes to addition with other objects, like vectors, I am little bit...
  44. Titan97

    Effect on equilibrium, addition of inert gas

    If inert gases are added at constant volume to an equilibrium mixture, the total pressure increases. But the mole fraction of the gaseous reactants or products decrease. Partial pressure ##p=x\cdot P## where P is total pressure and ##x## is mole fraction. How can you say that ##p## remains...
  45. Scorry

    Vector Addition. Where did I go wrong?

    Homework Statement A car is driven 225 km west and then 98 km southwest (45 degrees). What is the displacement of the car from the point (magnitude and direction)? Draw a diagram. Homework Equations Vectors have magnitude and direction. The Attempt at a Solution My attempt is attached. This...
  46. victorhugo

    Basic vector addition - my attempts

    The teacher does not want this homework back, I just want to learn because I love science "1) A golf ball at a mini golf course is hit 10m NE where it hits a barrier and travels NW for another 18m. What is the balls displacement from the tee?" square root(18^2)+(10^2)= 20.6 metres. Now for the...
  47. T

    ?Understanding Special Relativity: Speed Addition & Subtraction

    special relativity says speed can be additive and subtractive ,our motion influences the speed , i did not get this part .how can our motion influence the speed of other object ?and how can speed be additive and subtractive
  48. toforfiltum

    Solving potentiometer problem with addition of resistor

    Homework Statement The emf of a battery A is balanced by a length of 75 cm on a potentiometer wire. The emf of a standard cell, 1.02V, is balanced by a length of 50 cm. What is the emf of A? Calculate the new balance length if A has an internal resistance of 2 Ω and a resistor of 8 Ω is joined...
  49. victorhugo

    Stuck on vector addition and subtraction

    Hello, here is a couple of example problems I'm not sure how to do, if someone could please explain how to do it I would greatly appreciate it! Subtraction: "A river flows at 0.8 m/s. If a boat moves across the water at 2m/s at what angle should it point so that it moves straight across the...
  50. victorhugo

    Vector subtraction and addition questions

    I have a couple of really basic and easy worksheets for vector addition and subtraction, but I'm getting confused because I used the formula Square root of (A^2 + B^2) to figure out most of them (change in velocity is displacement / time interval) and I don't see where I need to add or subtract...
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