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. dbc

    Let's change the definition of 'weight'

    Since 97% of everyday weight scales (both in doctor offices and at home) measure our actual mass either in lbm and/or kg, and NOT force (lbf or N), then why does oxford choose to define weight to be relative? "a body's relative mass or the quantity of matter contained by it, giving rise to a...
  2. Minestra

    Definition of Success problems with projectile motion

    So I just got beat up by this question on my midterm. I'm not sure if these problems are always called definition of success but that is how my professor refers to them as. The question: (paraphrased) When you walk into your dorm room you like to throw your keys onto the center of your desk...
  3. A

    Exploring the Mathematical Definition of Time

    Is there a good mathematical definition of time?
  4. F

    I Definitions of the Riemann integral

    In some elementary introductions to integration I have seen the Riemann integral defined in terms of the limit of the following sum $$\int_{a}^{b}f(x)dx:=\lim_{n\rightarrow\infty}\sum_{i=1}^{n}f(x^{\ast}_{i})\Delta x$$ where the interval ##[a,b]## has been partitioned such that...
  5. alexmahone

    MHB Use the formal definition to prove that the following sequence diverges

    $\displaystyle s_n=\left(\frac1n-1\right)^n$ My attempt: For large $n$, the sequence oscillates between $e^{-1}$ and $-e^{-1}$ and therefore diverges. Now for the proof. Assume, for the sake of argument, that the sequence converges to $L$. $\exists N\in\mathbb{N}$ such that $|s_n-L|<0.1$...
  6. L

    Definition and alternatives for Von Neumann architecture?

    I have been studying about computers and found that they evolved from the basic mechanical devices with limited functions to the amazing machines we have today. Its all very new and interesting to me. I believe that programming is the act of writing an algorithm in a higher or lower level...
  7. M

    Definition of centripetal force

    Homework Statement Hi, If an object is undergoing uniform circular motion, then the net force is acting perpendicular to the instantaneous velocity, and this is called the centripetal force. However, if the object is moving in a circle but the magnitude of its instantaneous velocity is not...
  8. Z

    New Definition derivative for Horsepower

    There has been SO much talk of HP and HP vs torque, it can make your head spin. I've been trying to help with some clarification for those that seem to be very confused of the physics and concepts that i came up with a new "definition" to augment what is commonly read as the definition of HP...
  9. S

    B Understanding Spin: A Basic Explanation for Beginners in Physics

    I know that I'm kinda asking for a lot here, but can any of you give me, a person with lesser experience in physics, a basic explanation of spin? I've found out that a particle's spin can be compared to a transistor, but that didn't really tell me what it actually is. What does it define? For...
  10. M

    Prove a limit using epsilon-delta definition

    Homework Statement Proof that: ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2}## using the epsilon-delta definition of a limit. (Problem below) Homework Equations ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2} \iff \forall ε>0, \existsδ>0, \forall x ∈ \mathbb{R}\backslash\{-1\}: 0 < |x-1| < δ...
  11. W

    Define the notation used here in describing a series?

    Homework Statement "For the given series, write formulas for the sequences an , Sn, Rn and find the limit as n->∞ (if it exists) Homework Equations ∑∞1 ((1/n) - 1/(n+1) The Attempt at a Solution I know how to take the limit, that's no problem. I'm a bit confused about what an , Sn, Rn are...
  12. M

    What is the origin and meaning of the word rocket?

    I was wondering if there is an actual definition given by a recognised organisation over what is meant by the word "rocket". In case there is not, I wanted to reflect upon what do we really mean when we say rockets.
  13. Pepper Mint

    [SQL Server] Object Definition

    Hello experts, I would like to learn the implementation of object_definition function in SQL server. I'd like the one with 2 parameters. Could you help me ? Thank you.
  14. dumbdumNotSmart

    Rigorous Multivariable Limit Definition Problem

    Homework Statement Hey I'm trying to prove the rigorous definition of limit for the following function: Lim (x,y) approaches (1,1) of f(x,y)=(y*(x-1)^(4/3))/((x/1)^2+abs(x)*y^2) Homework Equations abs(x^2)<abs(x^2 +y^2) The Attempt at a Solution I know the rigorous definition of limit. I...
  15. S

    I Boas's definition of first variation

    http://www.utdallas.edu/~pervin/ENGR3300/Boaz.pdf see page 493 he said that first variation of I is δI = dI/dε * dε http://www.colorado.edu/ASEN/asen5227_offline/slides/292-334.pdf but this pdf said (see page 309) that first variation of I is δI = dI/dε * ε (y and I commute, α and ε...
  16. J

    MHB G o F = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)}

    So I have the following: F = {(1,3)(2,2)(3,2)(4,2)(5,5)} G = {(1,1)(2,3)(3,4)(4,5)(5,2)} Am I right in saying that F o G would be: F o G = {(1,3)(2,2)(3,2)(4,2)(5,5)(1,1)(2,3)(3,4)(4,5)(5,2)} If not, does F o G actually mean? Thank you.
  17. S

    I Definition of stress-energy tensor

    Hello! Why is the stress energy tensor defined as a (2 0) tensor? I understand that it needs 2 one-forms as arguments, but using the metric, can't we bring it to (1 1) or (0 2)? So is there is any physical or mathematical reason why it is defined as (2 0), or it is equally right to define it as...
  18. I

    B How does the delta ε definition prove derivatives?

    The exercises in my imaginary textbook are giving me an ε, say .001, & are making me find a delta, such that all values of x fall within that ε range of .001. The section that I'm working on is called "proving limits." Well, that is not proving a limit. All that's doing is finding values of...
  19. Math Amateur

    MHB Finitely Cogenerated Modules - Bland Definition 4.1.3, Page 105

    I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 4.1 on Generating and Cogenerating Classes ... ... In particular I am trying to understand and get a good sense of the notion of a module being finitely cogenerated ... Bland defines a finitely...
  20. S

    I Definition of "recurrence relation"

    The definition from the current Wikipedia article is a good start: My technical question is whether "each further term" is a function of only the values of the preceeding terms, or is it also a function of the index of the "further term"? For example, if we are given that the values of two...
  21. B

    Definition of torque - What is r?

    Whats is r ? knowing that formula is T = F x r... please help me. thank you!
  22. M

    B Definition of the limit of a sequence

    The definition of a limit of a sequence, if the limit is finite, is: lim n >infinity un (un is a sequence) = l <=> ∀ε> 0, ∃N: n > N => |un - l| < ε This just means that un for n > N has to be a number for which: l -ε < un < l + ε Now, I'm wondering, can't we just say: n > N => |un -l| <...
  23. P

    How do I cope with the transition from teenager to adult?

    I don't want to be an adult, this idea freaks me out and makes me feel old Is 18 still an adolescent or is considered adult? When are you an adult and no more an adolescent? 20? What's the difference between teen and adolescent? And how did you dealed with the teen-adult transition? Was it...
  24. Jianphys17

    I Do Carmo's book, chap2 Regular surfaces, definition 1.2 -- question

    On chapter over regular surfaces, In definition 1 point 2. He says that x: U → V∩S is a homeomorphisms, but U⊂ℝ^2 onto V∩S⊂ℝ^3. I am confused, how can it be so!
  25. nomadreid

    I Definition of Field: A Necessary & Sufficient Explanation

    The definitions I have seen of "field" seem rather unsatisfactory. Wikipedia starts off by saying that a field is any function with spacetime as its domain, but this seems awfully broad, since there are 2|ℝ| number of functions with spacetime as a domain. Further down, Wikipedia basically says...
  26. E

    Definition of a meaningless proposition?

    Homework Statement I know that if a proposition can not be evaluated then it is meaningless, but how about statement like this? 4+1. Homework EquationsThe Attempt at a Solution I think "4+1" itself is meaningless because it can't be evaluated. Thanks!
  27. P

    I Understanding Plasma: Definition, Properties, and Temperature Considerations

    So, on wikipedia is said that a plasma is an ionized gas, just that, but when we think about plasma we think that is hot, so here's the question: What is the right definition of plasma? Does being a ionized gas also imply being hot and then saying only that is an ionized gas is enough? I mean...
  28. P

    I Question about the formal definition of conservative force

    So, I was reading the mathematical description of a conservative force o wikipedia : https://en.m.wikipedia.org/wiki/Conservative_force and at the line "Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not...
  29. K

    A Understanding the Eigenframe: Definition and Importance

    What is an eigenframe?
  30. ChloeYip

    B Choosing Epsilon for a Limit Problem: A High School Student's Guide

    I have only encountered questions that f(x)-L that can be factorize to get a constant, and delta is epsilon divide that number, as a high school student. I have no idea how to choose a epsilon for this question. Thanks.
  31. mertcan

    A Christoffel symbol definition

    hi, I have seen that christoffel symbol definition or logic is shown in different ways. For instance, in first attachment ( RED box) you can see a normal vector (n) next to the christoffel symbol, but in second image everything is same except that there is a normal vector. Is there a confusion...
  32. J

    I Definition of force over an area

    I am reading the wikipedia article on the Cauchy stress-tensor. The article says that given some object, let ##P## be a point in the object and let ##S## be a plane passing through that point. Then "an element of area ##\Delta S## containing ##P##, with normal vector ##n##, the force...
  33. 1

    I Understanding the Definition of Cp and its Relationship to Cv: Explained

    Hi all, I'm working through a derivation of the general relationship between Cp and Cv and there's one point which is confusing me. I understand that and and that this implies the following: but isn't this equal to 0? Shouldn't the two partial derivatives on the right...
  34. D

    I Is that the definition of a lie group?

    I learned a lie group is a group which satisfied all the conditions of a diferentiable manifold. that is the real rigour definition or just a simplified one? thanks
  35. Firasf1dream

    Effective Compression Ratio Definition?

    hello everyone, i would like please to know what is Effective Compression Ratio for an RC 2stroke Engine that i have ? the value in the info is 9.7, so i need to know the meaning and what values are the best ? what is the range ?
  36. N

    B Vague definition of the word molecule

    The word molecule has several definitions, but which one is considered the right one? The biggest question is if a single atom is still a molecule. Some call a helium atom a (monatomic) molecule. But others state that a molecule is a bond between two or more atoms. Some also say a molecule is...
  37. J

    A Covariant derivative definition in Wald

    I'm working through Wald's "General Relativity" right now. My questions are actually about the math, but I figure that a few of you that frequent this part of the forums may have read this book and so will be in a good position to answer my questions. I have two questions: 1) Wald first defines...
  38. evinda

    MHB Using the Definition: Showing $u \in C^0 [0,1]$

    Hello! (Wave) I want to show the embedding $W^{1,p}(0,1) \subset C^0 [0,1]$. So we pick a $u \in W^{1,p}(0,1)$ and want to show that $u \in C^0 [0,1]$. Let $x_n \to x$. We want to show that $u(x_n) \to u(x)$. Since $u \in W^{1,p}(0,1)$ we have that $u \in L_p$ and $u' \in L_p$. And you...
  39. R

    VdP term in definition of constant volume specific heat

    Homework Statement I know that for constant volume ∂q=du and so du=Cv.dT However i don't understand how did we get to ∂q=du by neglecting the vdP term of enthalpy What I am trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I don't understand since the definition of enthalpy is...
  40. Z

    B Physics 101 refresher question -- Confused about the definition of a Joule

    we all know the equation for KE 1/2mv^2 you do this simple math and you get an number that is in KE units , Joules. so, why is the KE unit equation, 1 Joule = Kg x (m^2/s^2) ?? 1Kg traveling at 1m/s would have a KE of 1Joule, but using the KE equation, it would be 1/2 a Joule. why is...
  41. T

    B What is the definition of a plane?

    I've been thinking about the flat surface we call a plane. I've looked for definitions and none of the ones I have found satisfy me...in this respect...they seem dependent on assumed meanings and not self-dependent using only geometric contructions. Let me explain. One definition of a plane...
  42. Falcus

    I Definition of a Lorentzian Wormhole

    I was reading into traversable wormholes when I came across this definition from Matt Visser; 'If aMinkowski spacetimecontains a compact region Ω, and if the topology of Ω is of the form Ω ~ R × Σ, where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form ∂Σ...
  43. L

    B Quantum definition of information

    Watching a physics documentary I heard the following statement 'If an object falls into a black hole, what happens to its information'. I have a problem understanding the definition of information Is this. Information we could have gained through study? Or, Information governing particles at...
  44. Tony Stark

    Work: Definition & Explanation

    Can work be explained in following context- Work done is the amount of energy exchanged in executing an action through non-spontaneous method.
  45. bananabandana

    Understanding the Uniform Probability Distribution in Statistical Ensembles

    Homework Statement Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct] The Attempt at a Solution This is what I understand so far: [/B] For any given...
  46. terryds

    Limit problem (by definition I think)

    Homework Statement ##f(x)=12x^2-5## The value of ##\lim_{h\rightarrow 0}\frac{f(x+2h)-f(x-3h)}{6h}## is ... A. 8x B. 10x C. 12x D.18x E. 24x Homework Equations ##f'(x) = \lim_{h->0}\frac{f(x+h)-f(x))}{h}## The Attempt at a Solution [/B] Looking at the problem question, it seems that it's...
  47. I

    I Why use a subset in the definition of bounded above?

    Is the subset ##E## necessary in the following definition? It doesn't seem to serve any purpose at all and could've been written with ##S## directly? Isn't ##E## just another ordered set since it's a subset of ##S##? Definition: Suppose ##S## is an ordered set, and ##E \subset S##. If there...
  48. ali khotbesara

    Definition material at MCNP(4c) code

    Homework Statement gamma beam (γ) consequent of co 60 [this source have two beam; 1.1732mev(99.88%) & 1.3325mev(0.12%)] radiation behind the concrete block [ 300×300×20 cm] (thickness is 20 cm). analysis and plot Gamma-Ray Attenuation at 5 cm layers (4 layer) and plot spectrum of exited...
  49. S

    Resistance: Definition & Difference Explained

    My professor says resistance depends on, R\quad =\quad \frac { \rho L }{ A } And is defined as, R\quad =\quad \frac { V }{ I } What does she mean? What is the difference? A definition is denoted by \equiv, what is the difference between that and an ordinary equal sign?
  50. J

    What is the definition of proper time interval according to the book?

    Hi guys, I'm having trouble understanding the definition of proper time interval, according to my book (Physics for scientists and engineers with modrn physics 10th edition serway jewett) the proper time interval "is the time interval between two events measured by an observer who sees the...
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