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. S

    Which equation is used to define resistance?

    Homework Statement What is the definition of resistance? a. Resistance is the potential difference per unit current b. Resistance is the gradient of the graph of potential difference against current c. Resistance is the voltage required for a current of 1 A d. Resistance is defined by the...
  2. WilliamMGiraldo

    B Common Time: Explaining Einstein's Definition

    Hi. Thanks for letting me ask this question. It is a stupid one. I'm a newbie at relativity theory, and I'm reading On the electrodynamics of moving bodies, By Einstein, A. He associates time with space, and tells us that you can measure the "time" of an event if you are in the coordinates of...
  3. entropy1

    B Is there a definition of randomness?

    Is there a definition of "random(ness)"? Is it defined?
  4. parshyaa

    Problem with the Definition of work

    From Newton's 2nd law F = ma and a = F/m(acceleration and mass are inversely related when force is constant) But in w = F.d , F =w/d(but d and F are not inversly related just as above) I think there's something wrong in my question, please point it to me or please answer it.
  5. A

    I What is the formal definition of a Universality Class?

    Hi guys, I have been reading some of the literature recently concerning the Kardar-Parisi-Zhang equation and the words "universality" and "KPZ universality class" keep appearing. I already did a cursory wikipedia search on the subject, but it did not make much sense to me. Can you please...
  6. J

    I Definition of Vector Field in General Relativity

    In general relativity we demand that the physical law can be stated as a form which does not depend on the choose of particular coordinate system, So the vector field is defined as a changing object following a regular pattern under the transformation of coordinates. For example, we can define...
  7. L

    Newton´s second law: Force definition? (Philosophy matter).

    Hi people! A may be philosophical question, in fact my doubt comes from epistemology class: Newton´s second law is a definition of force based on 2 previously defined things: momentum and time or is a relation found by Newton between 3 previously defined things: force; momentum and time? Thanks.
  8. Math Amateur

    MHB Differentiation of Vector Valued Functions and Affine Maps - Browder, Definition 8.9 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... I need help in fully understanding Browder's comments on Definition 8.9 ... ... Definition...
  9. L

    A General definition of interferences clarification

    I require your help to list all phenomena described as interferences in physics ( as teached nowadays ) with their citations in scholar documents if they are not well known by non-specialists. I am open to adjacent domains like information theory and mathematics. There are already light...
  10. L

    I How many generators can a cyclic group have by definition?

    Hi, so I have just a small question about cyclic groups. Say I am trying to show that a group is cyclic. If I find that there is more than one element in that group that generates the whole group, is that fine? Essentially what I am asking is that can a cyclic group have more than one generator...
  11. Euler2718

    Proof of sequence convergence via the "ε-N" definition

    Homework Statement Prove that \lim \frac{n+100}{n^{2}+1} = 0 Homework Equations (x_{n}) converges to L if \forall \hspace{0.2cm} \epsilon > 0 \hspace{0.2cm} \exists \hspace{0.2cm} N\in \mathbb{N} \hspace{0.2cm} \text{such that} \hspace{0.2cm} \forall n\geq N \hspace{0.2cm} , |x_{n}-L|<...
  12. V

    Mathematica Definition function with variable in name

    Hello, I would like to create few functions in loop by Table (not ordinary change a parameter, but different numerical solution of problem). The names should differ by "number"of the step, let's say "i", in the name. I.e. I would like to get set of function f"i"={f1=Interpolation[data]...
  13. R

    Definition of Momentum in terms of a partial derivative

    Dear Members, I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture. I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have...
  14. S

    A Lattice non-perturbative definition

    Dear All I would like to understand a paper for Xiao-Gang Wen " A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model" . Can anyone help me by suggesting another reference that is a little bit easier. Thank you
  15. N

    I What is the definition of a matrix in function form?

    My teacher told me to find the definition of matrix which is in function form, but haven't seen it. The definition of matrix that I know is a rectangular arrangement of mn numbers, in m rows and n columns and enclosed within a bracket, but it is not right which my teacher wants. I want to know...
  16. S

    I Definition of tangent space: why germs?

    I am reading "An introduction to manifolds" by Tu. He starts off in Chapter 1 by introducing some definitions on ##\mathbb{R}^n## that will carry across to general manifolds. In Chapter 1, 2.2, he defines germs of functions as a certain equivalence class of smooth functions ##C^\infty_p##. I...
  17. J

    B Force Defined: First vs. Second Newton's Law

    Can we say that the First law of Newton defines the force whereas the Second law gives the magnitude of force?
  18. K

    What is the Derivative as a Limit?

    Homework Statement Homework Equations Derivative as a limit: $$y'=\lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$ The Attempt at a Solution $$f'(x)=\lim{\Delta x\to 0}\frac{f(x)f(\Delta x)-(1+xg(x))}{\Delta x}=\bigstar$$ $$\left\{ \begin{array}{l} f(\Delta x)=1+\Delta x...
  19. Irfan Nafi

    General Definition of Potential Energy - Conceptual Help

    My textbook states that an alternative definition of the change in potential energy is the work required of an external force to move an object without acceleration between two points. I am confused on why it says acceleration. Wouldn't that mean that the acceleration is 0 and therefore the...
  20. Einj

    A Definition of [itex]\sigma_8[/itex]

    Hi everyone, apologies if this question has been asked already. My search didn't give any results. Can anyone tell me the definition of \sigma_8 in terms of the power spectrum? A reference where I could find it is perfect too! Thanks a lot
  21. M

    MATLAB Understanding the Prompt in Matlab: Commands and Terminology

    What is the definition of prompt in Matlab. Here is an example sentence. "commands are entered at the prompt with looks like two successive greater than signs" Are prompt and command window the same things in Matlab or all computer terminology? If so, is the prompt the environment where we...
  22. M

    B Volume of a Cube: Definition & Explanation

    Suppose if we have a cube: The volume of the cube is the product of the length, width and the height. All this time, I've been looking at it as: To get the volume, multiply the area of the cross section of the cube by how many "layers" it has. To elaborate with the diagram given, one can see...
  23. ecoo

    Reversed limit definition for monotonic functions

    Homework Statement Does the delta-epsilon limit definition in reverse work for describing limits in monotonic functions? By reversed, one means for lim (x -> a) f(x) = L if for each δ there corresponds ε such that 0 < | x-a | < δ whenever | f(x) - L | < ε. Homework EquationsThe Attempt at...
  24. J

    A Discrete measurement operator definition

    Consider the Gaussian position measurement operators $$\hat{A}_y = \int_{-\infty}^{\infty}ae^{\frac{-(x-y)^2}{2c^2}}|x \rangle \langle x|dx$$ where ##|x \rangle## are position eigenstates. I can show that this satisfies the required property of measurement operators...
  25. OcaliptusP

    Understanding Heat: Definition & Unit

    What is definition of heat? And why it's unit is kgm^2/s^2? I couldn't be able to link the unit to the definition.
  26. F

    I A question about the formal definition of limit

    Is it possible to learn to prove limits by the formal definition without doing a course of real analysis? I'm not talking about just following the model that the Calculus books give, what I want is to understand the why of all the steps in formally proving the limit, to understand the why to use...
  27. S

    I Definition of "equivalent" probability problems?

    Is there a precise definition for the statement that two differently worded probability problems are "equivalent"? One technique of (purportedly) solving a controversial probability problem is to propose an "equivalent" problem whose solution is not controversial. (e.g. The Sleeping Beauty...
  28. Math Amateur

    MHB Galois Theory - Fixed Field of F and Definition of Aut(K/F) ....

    I am reading Dummit and Foote, Chapter 14 - Galois Theory. I am currently studying Section 14.2 : The Fundamental Theorem of Galois Theory ... ... I need some help with Corollary 10 of Section 14.2 ... ... and the definition of \text{Aut}(K/F) ... ... Corollary 10 reads as follows: Now...
  29. Math Amateur

    I Galois Theory - Fixed Field of F and Definition of Aut(K/F)

    I am reading Dummit and Foote, Chapter 14 - Galois Theory. I am currently studying Section 14.2 : The Fundamental Theorem of Galois Theory ... ... I need some help with Corollary 10 of Section 14.2 ... ... and the definition of ##\text{Aut}(K/F)## ... ... Corollary 10 reads as follows: Now...
  30. A

    A Intution behind the definition of extrinsic curvature

    Forgive me for asking a rather silly question, but I have thinking about the following definition of the extrinsic curvature ##\mathcal{K}_{ij}## of a sub-manifold (say, a boundary ##\partial M## of a manifold ##M##): $$\mathcal{K}_{ij} \equiv \frac{1}{2}\mathcal{L}_{n}h_{ij} =...
  31. U

    Activity Definition: Is T Temp of Current State?

    The definition of activity is: $$\mu _{i}=\mu _{i}^{0}+RT\cdot \ln a_{i}$$ where μi is the chemical potential of i in current state and μi0 is the chemical potential of i in standard state. The current and standard state have the same temperature or can their temperature differ? If their...
  32. AlphaLearner

    Electric Flux Questions (about the definition)

    I can say that Electric Flux is Electric field passing per unit area perpendicular to electric field lines. But the formula came up as Φ = ∫ E⋅dA. Well, take the case of pressure! That is force acting per unit area perpendicular to direction of force. But it's formula came up as P = F/A. Now my...
  33. Math Amateur

    MHB Separable Polynomials - Paul E Bland's definition and example ....

    I am reading Paul E Bland's book: The Basics of Abstract Algebra and I am trying to understand his definition of "separable polynomial" and his second example ... Bland defines a separable polynomial as follows:https://www.physicsforums.com/attachments/6636... and Bland's second example is as...
  34. Math Amateur

    I Separable Polynomials - Paul E Bland's definition and exampl

    I am reading Paul E Bland's book: The Basics of Abstract Algebra and I am trying to understand his definition of "separable polynomial" and his second example ... Bland defines a separable polynomial as follows: ... and Bland's second example is as follows: I am uncomfortable with, and do...
  35. GregoryC

    B Absolute zero by definition is "nothing"

    Is absolute zero nothing? Can a quanta exist in nothing? There could be no quantum fluctuations at absolute zero.
  36. S

    I What is an Axiom? Definition & Examples

    Hello! I was wondering how does a mathematical statement come to be an axiom? I understand that an axiom can't be proven using other mathematical statements. But how does one know that a statement can or can not be proven? For example, why isn't Riemann Hypothesis considered an axiom? I also...
  37. M

    B The definition of a straight-line seems circular?

    Hi,I was just wondering if someone could provide clarity on this matter: that if a straight-line is initially defined as "a shape that forms the shortest distance between two points" and conceptualising that shape [that forms the shortest distance between two points] as one that, at an...
  38. M

    MHB What Is the Correct Way to Calculate the Probability of Flipping Heads?

    Probability of an event happening = (Number of ways the event can happen)/(Total number of outcomes) Please, explain the above definition How is the above definition applied to the following question. A coin is tossed 100 times. How many heads will pop up? Solution: Let P = probability...
  39. Avatrin

    I Motivating definitions in calculus on manifolds

    Hi I am a person who always have had a hard time picking up new definitions. Once I do, the rest kinda falls into place. In the case of abstract algebra, Stillwell's Elements of Algebra saved me. However, in the case of Spivak's Calculus on Manifolds, I get demotivated when I get to concepts...
  40. P

    B Definition of unshifted spectral lines?

    Hi, N00b question :-) I have read articles about redshift and blueshift and have a good idea about them. What I would like to know is how you decide if something is "unshifted" - what is the definition of this? is there a standardized way of defining/mapping an element's unshifted spectral...
  41. E

    Material definition problem in ANSYS Maxwell

    HI Guys, I am getting an error in Ansys Maxwell that says Maxwell2d solver, process solver2d: Internal Solver Error: 'In the Material: M270-35A_12 , the SLOPE of the End Two Points in this BH curve is 56519.1, which is more than 2 times of Mu0; This may lead to a non-physical solution...
  42. A

    I How does Einstein define simultaneity in his 1905 paper?

    It so happens that last night I was rereading Einstein's famous 1905 paper On the Electrodynamics of Moving Bodies. I think this is one of the most fascinating scientific papers in history, but some people say it's not at all clear. In any case I love reading Einstein's papers. Clocks...
  43. S

    B Blackbody Definition: Absorbs All Light & Emits Thermal Radiation

    Hello! I am not sure I understand the concept of blackbody. The definition is that it absorbs all the incoming light and doesn't reflect any. However, it emits thermal radiation. Isn't thermal radiation still EM radiation, so technically still light, just at another frequency? So if it emits...
  44. S

    A Signs in the definition of anti de Sitter spacetimes

    Consider the definition (https://en.wikipedia.org/wiki/Hyperboloid) of the hyperboloid in ##\mathbb{R}^3## with the metric $$ds^{2}=dx^{2}+dy^{2}+dz^{2}.$$ The one-sheet (hyperbolic) hyperboloid is a connected surface with a negative Gaussian curvature at every point. The equation is...
  45. L

    I Reference Frame Usage in General Relativity

    In the book General Relativity for Mathematicians by Sachs and Wu, an observer is defined as a timelike future pointing worldline and a reference frame is defined as a timelike, future pointing vector field Z. In that sense a reference frame is a collection of observers, since its integral lines...
  46. K

    Greatest Common Divisor Theorems definition clarification.

    Hi, I read definition of GCD theorem, from book and from mathWorld website. " There are two different statements, each separately known as the greatest common divisor theorem. This does not make sanse 1. Given positive integers and , it is possible to choose integers and such that ...
  47. N

    Euclidean and non Euclidean geometries problems

    So I was reading this book, "Euclidean and non Euclidean geometries" by Greenberg I solved the first problems of the first chapter, and I would like to verify my solutions 1. Homework Statement Homework Equations [/B] Um, none that I can think of? The Attempt at a Solution (1) Correct...
  48. G

    Definition of efficiency of a thermodynamic cycle

    Hi. Sorting the exchanges of heat and mechanical work in a thermodynamic cycle by the signs and summarizing, I get ##Q_{in}>0##: heat transferred into the system ##Q_{out}<0##: heat transferred to the cold reservoir ##W_{out}<0##: work done by the system ##W_{in}>0##: work done on the system...
  49. L

    MCNP volumetric source definition

    I am now in the process to define a cubic volumetric source in mcnp code, does anyone have a clear explanation for that.
  50. E

    Definition of 'with the vertical' in this question?

    Homework Statement (please ignore something that is not english) Homework Equations ac=v^2/r Fc is about 6.0E3 N and ac is about 5.0 m/s^2 (b) is the problem... The Attempt at a Solution what is 'with the vertical' here? the direction/opposite of ac or the direction of v?
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