# What is Addition: Definition and 651 Discussions

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. ### Vector addition, trying to find the angle

Is angle Vag 180 since the vector is a straight line pointing left? Also you can add 30 degrees with 150 which will be 180?
2. ### A Addition of two velocities

I am going through https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf, here I don't understand how we wrote eq. 1.5.3 with the help of three-vectors to get eq. 1.5.4.

4. ### B Understanding Dedekind Cuts: Exploring Addition and Negative Numbers

This is a really basic stupid question but has me beat. I am almost certainly missing something but for the life of me cat see what. If A and B are are the lower sets of two Dedekind cuts addition is defined as the sum of the elements (r+s) with r in A and s in B. Is that correct or have I...
5. ### B Are there two kinds of inverse with respect to closure?

For every instance of addition or multiplication there is an inverse, closed on the naturals. Not every instance of subtraction and division is defined, so not closed on the naturals. This looks like two kinds of inverse. Instance inverse - the inverse of instances of addition and...
6. ### Does the book have an error in the addition of these two vectors?

(a) $$\vec A = -\vec M+2\vec N=26\hat a_x+10\hat a_y+4\hat a_z$$ Unit Vector Formula $$\hat a_A=\frac{26\hat a_x+10\hat a_y+4\hat a_z}{\sqrt {26^2+10^2+4^2}}$$ $$0.923\hat a_x+0.355\hat a_y+0.142\hat a_z$$ The book gives ##0.92\hat a_x+0.36\hat a_y+0.4\hat a_z## Not sure how the book get 0.4 for...
7. ### Simple Addition of Vector Forces on an Eye-Hook

The screw eye is subjected to two forces, F1 and F2. Determine the magnitude and direction of the resultant force.

The solution (green arrow) states that for example : 0xD + 0x9 = 0x16 Details : 0xD = 13, 0x9 = 9, 13 + 9 = 22, 22 = 0x16 Where does the 0x16 come from? I do get to add D + 9 = 13 + 19 = 22 so how come 22 is equal to 16 (assuming D + 9 = 16 is correct) How am I suppose this solution?
9. ### B Relativistic Velocity Addition: Is c Ever Exceeded?

I was watching this video by Brian Green about relativistic velocity addition when he said something at the end that I wondered about. https://www.britannica.com/video/222286/Your-Daily-Equation-07-Relativistic-Velocity-Combination It was along the lines of the formula will always result in...
10. ### Comp Sci Is it addition or xor in AES mix column?

https://www.networkdls.com//Articles/AESbyExample.pdf I'm confused because there are lots of XOR in this case. And I am not very technically aware when we'd XOR vs when we'd add. I just follow the guidelines given in standards. But here I got confused in page 9 of that pdf. When we do B7+4B...
11. ### Linearity and non-linearity in addition and multiplication

Hello friends. Excuse my ignorance. Why is addition linear and not multiplication?
12. ### I Velocity addition via k-calculus

We had a thread a while ago where a poster was particularly interested in the SR rule of velocity addition. And in that thread, I suggested a better foundation was the k-calculus approach, with a reference to Bondi's treatment in "Relativity and Common Sense". Here I would like to show how to...
13. ### I Applying Velocity Addition in Rotating Frame: Is It Correct?

From the top of my head, I would say that yes, the very moment our clocks are aligned, and the two bullets are launched it is perfectly ok to use the relativistic velocity addition formula to determine the speed of the bullets from my reference frame. But the more the disk keeps rotating, the...
14. ### I Relativistic Velocity Addition: Calculating Electron Speed

If we imagine launching an electron wave in a reference frame S with speed v, should someone viewing the electron from frame S1, which is in inertial motion referring to S, use the relativistic velocity addition to calculate the speed of the electron?
15. ### Understanding Velocity Addition Laws for People on Train & Ground

I kind of just made up the questions. I realize this is a basic question but my knowledge of physics is very limited.q1 answer v_left_ball = v_left_ball - v_train v_right_ball = v_right_ball + v_train q2 answer To get the speed from Bob's frame I would use v_Bob = v_Bob + v_Alice To get the...
16. ### Chemistry Addition of Grignard on an ester

Hi, I have a question regarding these 2 possibilities: Why does the addition of RMgX on an ester always form a ketone? We could very well have that tetrahedral intermediate without eliminating the alcoolate group no? Since your reaction pretty much always tend towards the formation of a weaker...

Adopt the speed of light equals one. Calls ##cos = c##, ##sin = s## $$ux' = \frac{v-uc}{1-uvc}$$ $$uy' = \frac{us}{\gamma(1-uvc)}$$ $$tan \theta' = uy' / ux' = \frac{us}{\gamma(v-uc)}$$ So that's basically my solution. The problem is: The answer is ##\frac{us}{\gamma(v+uc)}##. Now, i can't...
18. ### I Multiplication and addition definition of congruence classes

The definitions of them seem like arbitrary choices or an abuse of notation. I wonder what the reasons behind the definitions are. Thanks. PS. My instructor said such defs simplify the process of solving modular equations.
19. ### Velocity vector addition problem

Hello, guys. Interesting riddle here. I have no idea how to solve it. Tried different methods, but point is answer is always wrong, exact answer Downriver, at an angle of 53.13(degree) to the bank. That exercise is from "Pohl’s Introduction to Physics"

21. ### Where am I going wrong with this vector addition?

I am following along with an example in my book regarding force from an electric charge. I understand the process but I believe I am getting something wrong when it comes to adding the vectors. Essentially, F13 is equal to -1.35*10^-3 j and when I add that to the j component of F23 which is...
22. ### Compute relativistic addition of velocities

edit: I had a sign error that is now corrected, no further help needed. Consider in the laboratory frame one second passing. Let ##(t,x)## be the coordinates of various events in a spacetime diagram. Both particles are released at ##(0,0)## Then after one second the left moving particle is at...
23. ### B Misuse of Velocity Addition: Troubleshooting

Something seems wrong with my use of velocity addition: A fly of rest mass ## m_{0} ## in your reference frame (say a platform) is posed in a train passing with a velocity ## v ## relative to the platform. The fly mass is now for you ## m_{1} = m_{0} \gamma(v) ##. Now in the train the fly is...
24. ### Lorentz Velocity Addition Problem

So for the formula, u'=u/(δ(1-(uv)/c^2) u=2.06E8 and v=0. I am only looking at the y components here. Since v=0 it really becomes u'=u/δ or u'= u*sqrt(1-(u^2)/c^2)). Anyways when I plug this in I am getting 1.49E8 when the answer should be 0.951E8. Am I not using the correct formula here?
25. ### Stargazing Roberto's Indonesian Punggur Meteorite: My 2021 Collection Addition

A new meteorite into my collection from Roberto Vargas (USA) - The Indonesian Punggur, first fall for 2021 (Jan 28) 1.2g of awesomeness, high iron breccia Thanks so much buddy, much appreciated

27. ### Velocity addition formula in X and Y axes (Relativity)

The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...

Velocity addition paradox: In observer A's frame, observers B and C move away from him at the speed of light c, B to the left and C to the right. In B's, frame A and C are both moving away from him at c, i.e. at the same speed. In both A's and C's frames they are moving at different speeds...
29. ### I Velocity Addition and Doppler Effect: Explained

The Doppler effect of light corresponds to the classical Doppler effect corrected by time dilation, but the first one is obtained with classical velocity additions (c+v at the front of the source and c-v at the back) whereas velocity addition of special relativity gives c at the front and c at...
30. ### B Experimental Confirmation Length Contraction Velocity Addition

What if any is the experimental confirmation for length contraction and the velocity addition formula?
31. ### MATLAB Simple addition of vectors of different lengths

I want it to be able to add vectors of different length with a 'shift' of c, and where elements do not align to assume a zero in the place of that, My function is: %c is the parameter shift function[sum]=vecadd(y,b,c) p=length(input) q=length(a) if p > q for i= 1+delay:p+delay...
32. ### Vector Problem -- Addition of two vectors given in polar coordinates

Doing a review for my SAT Physics test and I'm practicing vectors. However, I am lost on this problem I know I need to use trigonometry to get the lengths then use c^2=a^2+b^2. But I need help going about this.
33. ### Group theory with addition, multiplication and division

Hi everyone, I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track. If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...
34. ### An addition to respiratory Personal Protection Equipment

Hello all : i am asking if there is a class of respiratory protective equipment , that can be installed inside the human body to support the normal PPE and reduce the possibility to getting infected buy some biological agent : as virus size is between 50 to 160 nm , and the first area of...
35. ### Addition of moments of inertia

Hi To calculate the moment of inertia of a large sphere , I can calculate I for a smaller sphere and then add to it , I for the spherical shell that added to the smaller sphere makes the larger sphere. Does this general process apply to all shapes ? If so , does this process have a name ie. is...
36. ### MHB Addition of two sinusoids

So I have figured out two equations model a Ferris wheel ride(two different ferris wheels). F1 = Ferris wheel one F2= Ferris wheel two F1, h=-12\cos\frac{\pi}{10}t+12.5 F2, h=-12\cos\frac{\pi}{30}t+15 Now from these two equations, I want to know when F2+F1= 27.5m i.e I want to find the...
37. ### I Addition of Cosmic Velocities: Expansion Equation & Horizons

The expansion equation of the universe be ##\dot{R} = f(R)##. There shall be a photon at distance ##x## from us moving directly towards us along the line of sight. Are the velocities to be simply added, so the photon has speed ##f(x) -1## relative to us (local velocity of light set unity)? This...

Now following is my attempt for the very first one. Let ##\arctan(x) = \alpha## and ## \arctan(y) = \beta ##. So, I have ## x = \tan(\alpha)## and ##y = \tan(\beta)##. Since the domain is restricted to define inverse function, I have that ##\alpha \in (-\pi/2, \pi/2) ## and ##\beta \in (-\pi/2...
39. ### B Velocity Addition: Unraveling the Mystery

I keep getting into these discussions and finding out they are not as simple as I thought. Or at least, my math is rusty. Scenario A: Two ships are each receding from Earth at .9c in opposite directions. Since these are velocities, they should have opposite signs. That can't be right, since...
40. ### I Proof of addition of limits when the output value is infinite

I was looking at some websites that show the proof of addition of limits for a finite output value, but I don't see one for the case of infinite output value, which has a different condition that needs to be met - i.e., | f( x ) | > M instead of | f( x ) - L | < ε...
41. ### Calculating Moment: Addition of Torque Components

First of all, sorry for the units. This is a problem I found on the internet and am confused about the solution. I calculated the two components of the moment (torque) to be ##T_x = 18\times Fcos(30)## and ##T_y=5\times Fsin(30)## The problem is, I got the proper answer (the two options...
42. ### I Vector addition in spin orbit coupling

Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...

Determine the value of \frac13+\frac16+\frac1{10}+\frac1{15}+\frac1{21}+...+\frac1{231} I know that it means \frac1{1+2}+\frac1{1+2+3}+\frac1{1+2+3+4}+\frac1{1+2+3+4+5}+\frac1{1+2+3+4+5+6}+...+\frac1{231}, but how do I answer? It's from a student worksheet for 7th graders, so they haven't...
44. ### B Special case of relativistic velocity addition law

Hi gentlemen. My model is simple. Imagine, I watch a body which approaches me with velocity of w which value I can measure . I know that this a body has velocity v in a some reference system which aproaches me with same velocity of v. This velocity needs to be calculated (I can not mesure it)...
45. ### Addition of Harmonics in a string wave

In basic optics, we are given the general solution of the wave equation (massless string of length L) as a linear combination of normal modes, that need to have some of the permitted frequencies due to boundary conditions. In laboratory, we observed that phenomenon. We generated a wave in a...
46. ### Solve velocity addition problems using 4-vector

I used the two equations above to solve for u_x and u_y and got u = 0.987c, where u_parallel = u_x and u_perpen = u_y. I wonder if I can use velocity four-vectors to solve this problem. Modify η'μ = Λμνην so we can use it for velocity addition?
47. ### Vectors physics homework -- Addition of two vector forces

Trying to solve it
48. ### I What is the addition law for probability with multiple elements?

The additional law with two elements can be expressed $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$, while the law with three elements can be $$P(A\cup B\cup C)=P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(A\cap C)+P(A\cap B\cap C)$$ Now I wonder if there is the more general form of addition law, which applies...
49. ### I Triangle law of vector addition and the Pythagoras theorem

i know its pretty basic but please give some insight for triangle law of vector addition and pythgoras theorem. becuase ofcourse if you use traingle law to find resultant it will be different from what is pythagoras theorem
50. ### Making a calculator program that can calculate integer addition / subtraction

im trying to complete mips program code about a calculator program that can calculate integer addition / subtraction written using the MIPS assembler. im having hard times to debug this. The input is given to the array of Formula char (base address \$ s0) in the form of a formula. The null...