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. E

    B What is Energy? A Clear Definition and Explanation

    Hello there, I have heard countless times about the word energy, but I still don't know what exactly an energy is. Like for example, we know the definition of a physical quantity called velocity which by definition is change in displacement (so we can easily describe what a velocity is). We...
  2. Leo Liu

    Definition of potential energy

    Potential energy is generally a function of position vector ##\vec r## and it is defined as ##\int_i^f \vec F(\vec r)d\vec r=-U(\vec r) \bigg| _{i}^{f}=U(\vec r_i)-U(\vec r_f)##, where the force is conservative. Using the fact that the integral of force is also the definition of work, I obtain...
  3. F

    Velocity definition and parameter dependence

    Hello Forum, Limiting our discussion to 1D motion, it is clear that the concept of instantaneous velocity is defined as the covered displacement dx divided by the time interval elapsed dt: $$ v = \frac {dx}{dt}$$ However, mathematically, the velocity ##v## can be made to depend on any...
  4. S

    B What is Plasma? Is Tungsten Vapour a Gas or Plasma?

    What is "plasma"? How is a fluid measured to be either a gas or a plasma? Mercury boils at 359 Celsius (632 Kelvin). Mercury vapour is poorly conductive, little ionized (incidentally - monoatomic) and generally defined as a gas. However, tungsten boils at 5930 C (6203 K). Photosphere of Sun...
  5. M

    I Is There a Set Definition for Propositions in Propositional Logic?

    In propositional logic we study rules of logical inference from propositions, such as ## (p\rightarrow q) \leftrightarrow (\lnot q \rightarrow \lnot p) ##, or ## \lnot (p \land \lnot p) \leftrightarrow (p \lor \lnot p) ##. Do we ever define the set of propositions we are dealing with? Some...
  6. LCSphysicist

    Equation Alternatives for Young's Modulus

    I just found a definition to the Young modulus as: Is this a plausible representation of Y? That is, i know the definition , i don't think we can say this definition and the first definition is equal.
  7. Rongeet Banerjee

    What is the definition of cathode in the photoelectric effect?

    We know anode=oxidation=loss of electrons and cathode=reduction=gain of electrons but in the photoelectric effect the electrons are gained at the anode and lost at the cathode of the discharge tube? References: Anode, Cathode, Oxidation, Reduction
  8. J

    B What is the definition of a black hole?

    Hi All, This is my first post, so please bare with me and if I am going all wrong about, please let me know. The definition of a black hole according NASA; 'A black hole is a place in space where gravity pulls so much that even light can not get out'. Now I am not challenging this at all...
  9. S

    The mathematical definition of "wave"?

    Is there a standard mathematical definition for "wave"? What is the definition? Assuming that there is a definition, what are the mathematical definitions of the properties of waves? For example, how is the "group" of a wave defined? ( as in the "group" that has a "group velocity"). I'm not...
  10. S

    I Does the definition of cardinality assume distinguishability?

    Physics speaks of a set S of N "indistinguishable particles", giving the set S a cardinality but forbidding any equivalence relation that can distinguish between two particles. Is this terminology inconsistent with the mathematical definition of cardinality? Suppose ##S## is a set with...
  11. J

    Difference between abstraction layers and modularisation

    I understand abstraction to be the process of representing a system, concept or process in simple terms, leaving out finer details which may obfuscate the bigger picture. My understanding of layers of abstraction is that it refers to different depths of understanding of a concept where each...
  12. S

    Definition of temperature in weather reporting

    In my town, newspaper stories say we've had several days of record high temperatures. The stories report temperatures in the range of 107 F. However, on the same days, online weather reports show temperatures as high as 116 F. I think online weather reports use reports from amateur weather...
  13. S

    B Torsion tensor definition doubt

    Let's say we have any two covariant derivative operators ##\nabla## and ##\nabla'##. Then there exists a tensor ##C^{\alpha}_{\mu\nu}## such that for all covariant vectors ##\omega_{\nu}##,$$\nabla_{\mu}\omega_{\nu}=\nabla'_{\mu}\omega_{\nu}-C^{\alpha}_{\mu\nu}\omega_{\alpha}$$ Now I'm quoting...
  14. Adesh

    I Understanding the ##\epsilon## definition of this integral

    Integrals are defined with the help of upper and lower sums, and more number of points in a partition of a given interval (on which we are integrating) ensure a lower upper sum and a higher lower sum. Keeping in mind these two things, I find the following definition easy to digest A function...
  15. P

    Polarization of Scattered Radiation, motivating definition?

    Figure from Jackson, the ##0## subscripts indicate incident waves whereas the lack of subscripts indicate the scattered wave. Figure from Zangwill, the hat ##\hat{e}## vectors are for the incident electric field. We are dealing with unpolarized light so we have two orthogonal polarization...
  16. E

    A peculiar definition of work on Wikipedia

    I came across this here: Is this incorrect? If we setup any coordinate system and take torques about that coordinate system, then I would have thought we say the work done in that frame is $$W = \int_{C} \vec{F} \cdot d\vec{r} = \int_{C} \vec{\tau} \cdot d\vec{\theta} \quad \left( = \int_{C}...
  17. N

    Conceptual Definition of Intelligence

    Summary:: We are fundamentally wrong in our understanding of what intelligence is. Intelligence is believed to be some manner of product of the size and scope of computing. Fundamentally stupid way of thinking. Intelligence is a function of the relationship between the size of a computation...
  18. G

    MHB Derivative using the limit definition (without using L'Hospital's rule)

    Hello everybody, could you help me with this problem please? I have to find a derivative in x0 of this function (without using L'Hospital's rule): I used the definition , but I don't know what to do next. Thank you.
  19. Arman777

    I Four-Velocity: Geometric Definition

    In a formal manner the 4-velocity defined as ##\vec{u} = \frac{d\vec{x}}{cd\tau}##. Now this is also equal to the unit tangent vector of the worldline. My confusion is actually more geometrical. ##d\vec{x}## is the infitesimal distance between two points in the worldline and ##cd\tau## is the...
  20. fluidistic

    Optical Looking for a high definition DIY spectrometer

    Hello people, I am looking for a high definition DIY spectrometer website or resource. If you find a good one please let me know. I've watched several youtube videos about it, used both googles and duckduckgo but I am left unsatisfied. There are several things I do not understand, both about...
  21. nineteen

    What is the standard definition for what an "electric source" is?

    The syllabus states : "Explain that the potential difference which is needed to apply across any electric circuit to flow current is supplied by an electric source". To explain this and make notes, I want to first understand what an electric source particularly is. And how all those electric...
  22. hizballah_arham

    Definition of Rheology : Irreversible or not?

    In Agricultural Process Engineering(Third Edition) by S.M. Henderson and R.L. Perry, Rheology is described as "... the science that considers stress-strain relations where flow proceeds irreversibly with time. Creep in metals and concrete and the strength properties of fruits and vegetables are...
  23. G

    MHB How Do You Prove Limits at Infinity?

    Hi, can anybody help me with this two limits? I have to prove them by the definition of limit. Thank you in advance.
  24. C

    I Definition of a Degenerate Subspace (QM)

    I was learning about Degenerate Perturbation Theory and I encountered the term 'Degenerate Subspace', I didn't really understand what it meant so I came here to ask - what does it mean? will it matter if i'll say 'Degenerate space' instead of 'Degenerate Subspace'? and subspace of what? (...
  25. M

    B What Does it Mean When We Say the Universe is 'Flat'?

    When we say the universe is "flat," do we mean: 1) If you could hypothetically "zoom" out to the edge of the universe it would appear roughly as a flat like a sheet of paper with local fluctuations / bumps to indicate the presence of matter. 2) If we draw 2 parallel lines from 1 location they...
  26. M

    Engineering Power Loss Definition in a Damped Wave Equation (Skin Depth Problem}

    Hi, So the main question is: How to deal with power loss in E-M waves numerically when we are given power loss in dB's? The context is that we are dealing with the damped wave equation: \nabla ^ 2 \vec E = \mu \sigma \frac{\partial \vec E}{\partial t} + \mu \epsilon \frac{\partial ^ 2 \vec...
  27. sneakycooky

    Is this a good alternative definition of electron affinity?

    traditional definition of electron affinity: the amount of energy released by an element in its gas form when gaining an electron second definition?: the stability gained by an element in its gas form when gaining an electron (e.g. halogens are more stable after gaining an electron, and when...
  28. M

    MHB Check existence of limit with definition

    Hey! :o I want to check the existence of the limit $\lim_{x\to 0}\frac{x}{x} $ using the definition. For that do we use the epsilon delta definition? If yes, I have done the following: Let $\epsilon>0$. We want to show that there is a $\delta>0$ s.t. if $0<|x-0|<\delta$ then...
  29. S

    The definition of the proper time

    I wonder what is the proper time, the time passed on the train or the time of the observer? If there is another people on the train, we see the train as a frame, so is the time on the train the proper time or the time of rest frame?
  30. M

    A Definition of the IAU for the ecliptic plane

    How is the definition of the IAU for the ecliptic plane? In particular I am interested how the perturbations are treated. Neither the Earth nor the common gravity center of Earth and moon move on an exact plane around the sun. I found the IAU document “Adoption of the P03 Precession Theory and...
  31. Math Amateur

    MHB Continuity of a Function .... Conway, Definition 1.7.1 .... ....

    I am reading John B. Conway's book: A First Course in Analysis and am focused on Chapter 1: The Real Numbers ... and in particular I am focused on Section 1.7: Continuous Functions ... I need help with clarifying Definition 1.7.1 ...Definition 1.7.1 reads as follows: My question is as...
  32. F

    What is the Definition of Derivative and How is it Proved?

    Proof: By definition of derivative, $$f'(a) = \lim_{x\rightarrow a}\frac{f(x) - f(a)}{x - a}$$ exists and is finite. Let ##(x_n)## be any sequence that converges to ##a##. By definition of limit, we have $$\lim_{x_n\rightarrow a} \frac{f(x_n) - f(a)}{x_n - a} = f'(a)$$. By definition of...
  33. S

    I Component definition in curvilinear coordinates

    I'm watching this lecture that gives an introduction to tensors. If we have a coordinate system that's an affine transformation of the Cartesian coordinate system, then the projection of a vector ##v## (onto a particular axis) is defined as ##v_m = v.e_m## or the dot product of the vector with...
  34. F

    Universal Mapping Property of Free Groups: Definition and Proof

    Let ##S = \lbrace a, b \rbrace## and define ##F_S## to be the free group, i.e. the set of reduced words of ##\lbrace a, b \rbrace## with the operation concatenation. We then have the universal mapping property: Let ##\phi : S \rightarrow F_S## defined as ##s \mapsto s## and suppose ##\theta : S...
  35. BabyHueyTAW

    Definition: What is meant by port "CARP" ASIC functionality in a Field Programmable Gate Array?

    Summary: What is meant by port CARP ASIC functionality to a field programmable Gate Array FPGA. And what is Acronym CARP? What is meant by port CARP ASIC functionality to a field programmable Gate Array FPGA. And what is Acronym CARP?
  36. Johny Boy

    A Reduced Graph States: Characterizing Basis States

    Reduced graph states are characterized as follows from page 46 of this paper: Proposition: Let ##A \subseteq V## be a subset of vertices for a graph ##G = (V,E)## and ##B = V\setminus A## the corresponding complement in ##V##. The reduced state ##\rho_{G}^{A}:= tr_{B}(|G\rangle\langle G|)## is...
  37. W

    Figuring out "Definition" in Python 2.7 Anaconda Birthday Dictionary

    --- Say we have the dictionary in Anaconda 2.7 Jupyter :--- B={'A1':'Jan1' , 'A2':'Feb2',...} of Birthdates. ---I can call a name , e.g., 'A1' , using Birth[name]. As in :--- print('What is your name '\? ') name=input() print('Yes, Birth[name] is in our list') ---How do I call a Date? I want...
  38. C

    A What is the definition of 'ground state',considering H- ion = -14.35eV

    If 'ground state' is the lowest energy state, and H atom takes -13.6eV to ionise while H- takes -14.35eV, why is H- not considered the 'ground state'? Is that definition wrong? What is the definition of 'ground state' that "fixes" this?
  39. K

    I Wiki definition of Fermi coordinates

    Is the wikipedia definition of Fermi coordinates accurate? https://en.wikipedia.org/wiki/Fermi_coordinates
  40. K

    Help With MCNP Volume definition

    I need some help defining a tally volume. I want a volume bounded by three surfaces, but when I do an initial plot the volume is in red dashed lines. I know that each cell needs to be uniquely defined, but I am not seeing how my volume is not unique. The cell in question is cell 200 in the code...
  41. F

    I The new definition of kg and the mass-energy equivalence

    Hi, today I stumbled upon a 2016 article in Scientific American about the (then) possibility of re-defining the kilogram through Planck's constant. The article is really a very quick review of the topic. At some point the author states the following "So for years, physicists have chased an...
  42. V

    Finding Maximum Delta for a Limit Involving a Quadratic Function

    Consider limx→3x^2=9. Find a maximum value of δ such that: |x2 - 9|<0.009 if |x-3|<δ I just learned how to do this today and I am quite comfortable doing this if the function is linear, however now I am struggling with working with quadratic functions. So far this is what I have come up with...
  43. Coder Hashtag

    B What is the definition of angle?

  44. A

    B Basic definition: Nuclear Fusion & Fission

    The best-known classes of nuclear transmutations are fission and fusion: Nuclear Fusion Under normal condition, nuclei do not stick together; because they repel each other at large distances (due to the electrostatic repulsion 'barrier') and thus the strong nuclear force cannot act. But if these...
  45. haushofer

    A Issue with the definition of a Lie derivative and its components (Carroll's GR)

    Dear all, I'm having a small issue with the notion of Lie-derivatives after rereading Carroll's notes https://arxiv.org/abs/gr-qc/9712019 page 135 onward. The Lie derivative of a tensor T w.r.t. a vector field V is defined in eqn.(5.18) via a diffeomorphism ##\phi##. In this definition, both...
  46. E

    Definite and indefinite integration in the definition of work

    This is going to sound like a silly question, but here we go anyway! I've always thought about a definite integral being used for modelling a change in some quantity whilst an indefinite integral is employed to find the defining function of that quantity. For example, consider the...
  47. L

    I Understanding the definition of derivative

    As far as I understand, when we want to differentiate a vector field along the direction of another vector field, we need to define either further structure affine connection, or Lie derivative through flow. However, I don't understand why they are needed. If we want to differentiate ##Y## in...
  48. S

    I Is a Function Funny When Its Secant is Less Than a Certain Number?

    The definition Let a, b be any two real numbers Let c > 0 We define a function f to be funny iff For all x, y belonging to [a,b], |f (x) - f (y)| ≤ c |x - y| Question Let a < b (arbitrarily) Let c > 0 Assume function g is funny on [a, b] Let x, y ∈ [a, b] Therefore, |g (x) - g (y)| ≤ c |x - y|...
  49. W

    Is the Solar Constant Really 340 W/m^2 or 680 W/m^2?

    The solar constant is only on one side of the Earth, however it moves around and the Sun gives out it's energy/heat all over the Earth in 24 hours. And the seas and land have heated up over time. However I got told this, No its not. By definition the solar constant is referring to a 2...
  50. P

    A When and Why Was the Definition of the Meter Changed?

    The wording of the definition of the meter has apparently changed recently. I'm wondering about the motivation for the change. The current definition is: The older definition (1983, I think) was Does anyone know when and why the change was made?
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