What is Definition: Definition and 1000 Discussions

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the sense of a term) and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.

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  1. Ackbach

    Confusion on Body Definition in Y&F, 9th, 4-49.

    Homework Statement From Young and Freedman's University Physics, 9th Ed., Problem 4-49. Two blocks are connected by a heavy uniform rope with a mass of ##4.00## kg. An upward force of ##200## N is applied to the top block, which has a mass of ##6.00## kg. The lower block has a mass of ##5.00##...
  2. P

    Precise (Or Epsilon-Delta) Definition of a Limit

    Hello guys! I am trying to get a solid grasp of the Precise Definition of a Limit. I am having a particular hard time linking the intuition of the limit I developed a while ago to the Epsilon-Delta definition. I understand the basics: a limit exists/is only true if and only if for every...
  3. O

    Centripetal Acceleration definition help

    Hello, my textbook says that the magnitude of centripetal acceleration is equal to the sum of the forces acting on that object. (this is in regard to an object in a circular path, by a string. See...
  4. L

    Matlab - What does an array definition mean

    I'm trying to make a MATLAB plot with two types of data, i.e. temperature and air flow rate. Since the temperature and air flow rate are on different scales I wanted two y-scales and since there are quite some data sets, I wanted to make the two air flow rates bold. I tried this, but it doesn't...
  5. naima

    Are There Only 4 Bell States According to Wikipedia's Definition?

    I look at wikipedia.org/wiki/Bell_state and use the same notations. The article says that there are just 4 Bell states. Is not |\xi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |+\rangle_B + |1\rangle_A \otimes |-\rangle_B) another maximally entangled state? The Schmidt decomposition...
  6. S

    How can I use this hint to help prove the limit using the definition?

    Homework Statement Hello, I have to prove, using the limit definition, that \lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty The Attempt at a Solution I've set this unequation \frac{x-3}{x-1} < - M but it doesn't lead to the result 1<x<1+\frac{2}{M+1}, what did I wrong ? Thanks
  7. K

    Quick definition of an osculating plane

    I was absent to a calculus III lecture last monday. I didn't miss much, and have gone over what I did. I understand the work and know how to do the problems, the only thing I'm having trouble with is actually picturing what an osculating plane is. I just need a simple explanation of what it...
  8. T

    Sequences - Definition of convergence

    Alright, I need some help with this. an = \frac{1 - 5n^{4}}{n^{4} + 8n^{3}} To find the limit of convergence, use l'Hopital's Rule. The result will come out to L = -5 From my book, "The sequence {an} converges to the number L if for every positive number ε there corresponds an...
  9. B

    What is a D-domain and how is it used in AC machine systems?

    Does anyone know what a D-domain is and a D-domain partition?
  10. C

    Formal definition of quantum dot

    Is there a definition of quantum dot that everybody agrees? I searched intensively both from google and from web of science, but I couldn't find a formal definition. e.g (wiki says) A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions. confined but...
  11. N

    Understanding Parallel Lines: Definition and Differences

    Homework Statement The question states True or False: Two lines parallel to a third line are parallel Homework Equations You need to know the difference between skew, parallel and perpendicular The Attempt at a Solution I thought of three parallel planes (which have an infinite...
  12. M

    What is the significance of 'sufficiently large' values in Laplace Transform?

    In the attachment that I added I highlighted the portion I am questioning. I will define L[f(t)](s) to be the laplace transform of the function f(t). f(t) = e^t L[f(t)](s) = 1/(s-1). The laplace transform is defined for all values s≠1. L[f(t)](2) = 1. Question: "What do they mean by...
  13. F

    Thermodynamics: First law and work definition

    I've been having some doubts regarding the definition of work in thermodynamics and how it is related to the change of energy in the system. I have tried asking this in physics stack exchange but I was unable to obtain a satisfactory answer; now that I am trying again in this forum I will aim to...
  14. S

    Schwarzchild Radius: By definition must be dependent on distance.

    The Schwarzschild Radius of an object is the length such that if the object is shrunk down that small, the escape velocity becomes equal to the speed of light. That being said, however, the escape velocity of any gravitational body matters where it is measured relative to the center of mass...
  15. D

    Looking for an algebraic definition of work.

    Greetings and Salutations! Currently I am not enrolled in a physics class but I am researching on my own and I was wondering if there was an algebraic definition of work and what it was if it exists. The only definition of work I know of (cursory knowledge i.e. I saw the following words...
  16. G

    Time 'measurement' (or definition) for early universe

    We define time by the rate at which physical processes (i.e. clocks) tick. With atoms for example we can define time by their energy transition rates such as in atomic clocks. But, what before atoms existed? Current cosmology theories make statements such as that '0.5 seconds after the Big...
  17. P

    Verify the commutation relations for x and p by definition.

    Homework Statement Verify ##\left[ x^{i} , p_{k}\right] = i \hbar \delta^{i}_{k}## Homework Equations ## p_{j} = -i \hbar \partial_{j}## The Attempt at a Solution Writing it out i get $$ i \hbar \left( \partial_{k} x^{j} - x^{j} \partial_{k} \right)$$ The Kronecker makes perfect sense, it's...
  18. A

    Understanding Algebras: The Relationship Between Rings and Modules

    "Let R be a commutative ring. We say that M is an algebra over R, or that M is an R-algebra if M is an R-module that is also a ring (not necessarily commutative), and the ring and module operations are compatible, i.e., r(xy) = (rx)y = x(ry) for all x, y \in M and r \in R." I'm not really...
  19. F

    The definition and causes of the Coanda effect

    I am confused about the following points regarding the definition and causes of the Coanda effect: whether the Coanda effect is the same as normal boundary layer attachment to a surface whether the Coanda effect is only defined for convex surfaces over which a jet (of the same state as the...
  20. C

    Definition of a Magnet Period?

    I'm trashing the template here because I'm not looking for help with how to solve my homework problem. Instead, I'm looking for what my question actually means! I'm given an equation that describes a magnetic field. One of the specs I'm given is that the magnet period is 10cm. What in the...
  21. K

    Acid-Base Reactions: Is it Always a One-to-One Relationship?

    Lets say a certain chemical reacts with an acid. Does that make that chemical a base always and vice versa? Like in S + NaOH → Na2S + Na2S2O3, Sulfur reacting with a base would it make S an acid? Or do we call it a base or an acid, reacting with the opposite if it's producing water as a...
  22. C

    Definition of effective QED coupling.

    (PS: this post was also posted at the quantum mechanics/field theory forum, but I did not get any replies there) Often when one speaks about the effective QED coupling one defines it as $$e = \frac{Z_2 Z_3^{1/2}}{Z_1} e_0 \ \ \ \ (*)$$ when ##Z_1 = Z_2## by the Ward identity this...
  23. C

    QED running coupling definition.

    Often when one speaks about the effective QED coupling one defines it as $$e = \frac{Z_2 Z_3^{1/2}}{Z_1} e_0 \ \ \ \ (*)$$ when ##Z_1 = Z_2## by the Ward identity this turns out to be ##Z_3^{1/2}e_0## and some authors just define the coupling to be this right away. So why do some make a...
  24. C

    Scalar Definition: Transformations & Frames

    Is there conventional terminology to distinguish between scalars that transform between frames and those that don't? For example, energy is a single-component quantity but it isn't the same in every frame, whereas the length of a vector is also a scalar but is the same in every frame. Do we just...
  25. S

    I need the definition of a few basic physics terms. Can anyone help?

    So, I know this stuff is probably very elementary for most of the people on this site, but I have never had physics before, and I just started physics I at college. The professor has asked us to learn a few basic physics terms and I am having a hard time finding clear definitions for some of...
  26. F

    Formal definition of Dirac's delta and charge densities

    Hi, I'm new to this forum but I've been aware of its existence for a while and it's pretty cool. I finally came up with a question to post so here i am :) I've read a few nice posts on this forum about this topic, but I couldn't find the answer to what I'm looking for. I'm familiar with the...
  27. P

    Definition of transient absorbtion

    Hi, could someone help me to define what is transient or in other words short-lived absorbtion? Maybe the general defintion could sound something like: In transient absorbtion the sample is excited with some kind of source(electrons, laser ,x-ray and so on) and then flashed with wide spectra...
  28. B

    How Does Physics Unlock the Secrets of Everyday Phenomena?

    I'll go right to the point. I'm trying to get someone interested in physics (and relieve physics of adjectives like boring) . All I'm asking for is a clear, fun and kind of insightful way for looking at physics and how it relates to our daily lives and how it helps us understand our...
  29. M

    Definition of isometry in components form

    From the book of Nakahara "Geometry, Topology and Physics": A diffeomorfism ##f:\mathcal{M}\to \mathcal{M}## is an isometry if it preserves the metric: ## f^{*}g_{f(p)}=g_{p} ## In components this condition becomes: ## \frac{\partial y^{\alpha}}{\partial x^{\mu}}\frac{\partial...
  30. nomadreid

    Definition of (quantum) information?

    I am trying to find a consistent, non-circular definition of information, which includes quantum information. The two main definitions that recur are the von Neumann entropy and the superposition definition. Let's take the latter; the former is similar. This would mean that any change in the...
  31. 7

    Definition of a wavefunction as a function of position.

    Hello i wonder if anyone here can explain to me, why the wavefunction as a function of position is defined like this: $$\Psi(x,t) = \langle{x}|{\Psi(t)}\rangle$$ Why is it wise to use an inner product as a definition?
  32. C

    MHB Proving Definition of Continuous Function: Hi, Carla!

    Hi, I have my exam tomorrow and have been doing the practice questions. However we don't get the answers to these questions so I am lost as to whether I am doing them right, also I am stuck at a few points, particularly with the definition questions. \[ 1.)Prove\ lim_{x \to...
  33. T

    Group definition for finite groups

    Was wondering if the only required definition for finite groups is closure (maybe associativity as well). It seems that is all that is necessary. The inverse and identity necessarily seem to follow based on the fact that if I multiply any element by itself enough times, I have to repeat back to...
  34. A

    Definition of Force confused about how it includes direction

    In early physics, i learned a force was simply a push or pull, talked about as a number of Newtons or pounds, such as "the force is 5lbs". Then you learn that a force is really a vector quantity, having both the direction and strength/force, so it should be "5lbs to the east or 15lbs...
  35. Astrum

    Definition of Integral in Multiple Variables

    Dyadic Cube C_{k,N} = X \in\ \mathbb{R}^{n} \frac{k_{i}}{2^{N}} \leq x_{i} < \frac{k_{i}+1}{2^{N}} for 1 \leq i \leq n Where k = \pmatrix { k_{1} \cr k_{2} \cr \vdots \cr k_{i} \cr } I understand that N is the level of the cubes, but what does k equal? I'm having trouble...
  36. V

    Define Individual Forces Acting on a Body

    0k i know net force on a body is defined as mass times acceleration of the body w.r.t inertial frame, but how do we define individual forces acting on the body? Eg. Forces acting on a 1kg block are F1=+6¡ And F2=-4¡ So we know net force=2¡, and net acceleration=2 m/s^2 but how do we actually...
  37. P

    Derivative using first principle definition

    Homework Statement Calculate the derivative of f(x) = x^3 - 3x^2 Homework Equations (f(x+h) - f(x))/h The Attempt at a Solution Just wondering if someone can check my solution. (f(x+h)- f(x))/h= ((x+h)^3- 3(x+h)^2- (x^3-3x^2))/h = (x^3+ 3x^2 h+3xh^2+ h^3-3(x^2+ 2xh+ h^2 )-...
  38. M

    Definition of liminf of sequence of functions?

    Homework Statement Hi I've come across the term lim inf ##f_n## in my text but am not sure what it means. ##\lim \inf f_n = \sup _n \inf _{k \geq n} f_k## In fact, I am not sure what is supposed to be the output of lim inf f? That is, is it supposed to return a real-valued number, or a...
  39. B

    Multilinear Algebra Definition

    I'm reading Lee's Introduction to Smooth Manifolds and I have a question on the definition of a multilinear function Suppose V_{1},...,V_{k} and W are vector spaces. A map F:V_{1} \times ... \times V_{k} \rightarrow W is said to be multilinear if it is linear as a function of each variable...
  40. J

    What Does F >= g Mean in a Function Definition?

    Here's something which always manages to throw me in doubt. When one defines a function f to be greater than or equal to (or strictly greater) some other function g, So f >= g / f > g over some interval [a,b] simply speaking. Does this mean that for any value x in [a,b] : f(x) >= g(x)? OR...
  41. nomadreid

    Definition of species under attack?

    I learned that two sexual organisms are considered different species when no two organisms having their respective DNA structures could interbreed to produce viable offspring. Put another way, when looking it up, I find the definition: But then I read that: (a) Neanderthal interbred with homo...
  42. A

    What is the Definition of Current?

    While doing some questions using Kirchhoff's laws, I came across this problem, as shown in the picture. Obviously, no current passes through the 5 ohm resistor. But then I get confused. 1) If "no current" passed through the branch, wouldn't that be as if the branch weren't there? that would...
  43. N

    Definition of Thermal Energy?

    Hey guys. From my understanding, Temperature is a measure of the average kinetic energy of the molecules within a substance. Heat is the transfer of thermal energy between a system and its surroundings Internal Energy is the total energy (kinetic + potential) of the molecules of a...
  44. A

    By definition the space time fabric must have mass.

    Hello all, My post involves the unexpected continued expansion of the universe. As if matter is being accelerated by some means of unknown repulsion. Let us assume that current space time theory is correct. And that there is a "fabric" of space. We are all familiar with the grid...
  45. aleemudasir

    How far is this definition of time correct?

    How far is the definition of time that time is change in space, correct?
  46. N

    Understanding Current: Definition and Comparison to Math-Defined Current

    This is a very sound stupid question, but I'll go ahead anyway. Current is defined as the displacement of charge through a cross-section of a conductor per unit time. Okay. But how does relate to its math-definition, current = change of charge with respect to time, I=dQ/dt? I mean, for every...
  47. phoenixthoth

    Definition of mathematical object

    definition of "mathematical object" ...And "mathematical existence." Do these phrases have accepted definitions? Back when Dedekind was rejecting Cantor's transfinite ideas, could there have been a definition Cantor would refer to and say definitively "my (infinite) sets have mathematical...
  48. S

    Kinetic Energy Formula definition explanation

    Homework Statement I'm trying to understand how this equation was came together, mainly, I hardly understand why velocity is squared, and why there's the constant of '1/2'. Homework Equations In classical mechanics, the kinetic energy of a point object (an object so small that its mass...
  49. T

    Definition issue frequency domain - Random Signal Processing

    Hello i have a question about Random Signal Processing and the frequency domain. If i understand correctly one cannot use the Fourier transform to represent a stochastic process in the frequency domain. What is therefore used is the Power Spectral Density: S_X(f)=F\{R_X(\tau)\} Were F...
  50. S

    Tensor: Definition, Examples & n,m Meaning

    I was reading this page: http://en.wikipedia.org/wiki/Tensor which said the definition of a tensor was a relation between two vectors. I then went down to the examples section and it had some sort of (n,m) notation. I had some theories on what they meant but none of them made sense. What do n...
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