What is Definitions: Definition and 273 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. T

    Simple & Connected Graph Definitions for Exam Tomorrow

    just need 2 definitions without proof for an exam tomorrow, don't need to use them for anything just need to be able to quote them but can't find them anyway so if someone could helpfully write them down that would be great 1)simple graph 2)connected graph cheers
  2. D

    What are the key definitions in Linear Algebra?

    Hey guys, I'm new to physics forums I decided to join after seeing how you guys help each other. Well here's my problem I'm sure you guys can answer this. Last semester I had Linear Algebra and I slacked (almost failed) off a bit since it was a 8am lecture and it took place in a movie...
  3. H

    Exploring the Kinetic Energy Formula: Theorem and Definitions

    This theorem (if it is proven) comes also from a formula of kinetic energy. Has anyone some suggestions about this one. Definition of f(n): \ f(n)=(2^{n-1}a)Mod(a+b) Definition of g(n): \ \ g(n)= 4f(n)-2(a+b)+1 Definition of h(n): \ h(n)= Sign(f(n))(Sign(g(n))+1)...
  4. J

    Sudden confusion about definitions of singular homology

    Hi. I'm currently doing a course on algebraic topology and thought I was getting on great, was usually getting full marks on homework etc. But I've just got onto a question which should be fairly easy but its suddenly made me realize how badly I understand singular homology. Basically, it says...
  5. T

    Finding a Book on Manifolds: Definitions and More

    Please: I need abook that include this Definitions: 1- Manifold 2- Stable Manifold 3- unstable Manifold thank you.
  6. T

    I cant see the logic of thes definitions

    http://img21.imageshack.us/img21/3070/11650282.th.gif on the limsup case each time we take out the biggest member of the sequence . so it goes to the smallest memeber how its supposed to be the supremum of the limits
  7. C

    Finding Formula for recursive definitions

    This is the last part of the problem and I just can not figure out a formula for it. Here is what the question asks: Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well...
  8. T

    Why are there 2 definitions of Magnetic Moment?

    Hello everyone, this is my first post at Physics Forums! I am trying to understand electromagnetism, and when it comes to the magnetic moment, when reading around I see \mu = IA where A is area of a loop, which is an expression I can sort of understand. But when reading about magnetic drifts...
  9. Fredrik

    Definitions (continued from the cosmology forum)

    This is a reply to a comment made in the cosmology forum. That's not correct. Do you really believe that physicists are that dumb? The real story goes something like this: The speed of light is a constant in the real world. Therefore, we define a mathematical model in which the speed of...
  10. P

    Hypothesis, theory, model, and law definitions

    I think this merits its own discussion so I am creating a new thread for it. This was broken off from the Completeness of Quantum Mechanics thread. -MIH If it is labeled as a theory then whatever it is describing has been tested hundreds of times, generally finding the same result each...
  11. Q

    What is the best resource for learning set theory definitions?

    Hi all :D, Is there a website or book that has the definitions of most mathematical concepts in terms of sets? Thanks Q
  12. M

    Chemistry Definitions: Accurate & Concise for Tests

    I've been learning chemistry for a good while and now I'm doing it in college and what I've noticed is I don't do well in tests because I have trouble explaining what I know. Even though I understand the concept my answers aren't always adequate and I lose marks. Can anyone recommend a site that...
  13. M

    Recursive Definition of a Sequence: Solving for a5

    b]1. Homework Statement [/b] Given a0=1 and a1=2, and an=3an-1+an-2 for n>=2, calculate a5 recursively Homework Equations The Attempt at a Solution a5=3a4+a3 =3(3a3+a2)+a3=10a3+3a2 =10(3a2+a1)+3a2 =33a2+10a1 =33(3a1+a0)+10a1 =99a1+33a0+10a1 =109a1+33a0
  14. E

    Limit Superior - Equivalent Definitions

    Let a_1, a_2, ... be a bounded sequence of real numbers. According to Rosenlicht's "Introduction to Analysis", the limit superior is defined as sup {x : a_n > x for infinitely many n}. It is very hard to work with this definition. I'm used to the simpler one: sup {a : there exists a...
  15. D

    Understanding Norms: Why is f(0) = 0 Necessary?

    Homework Statement http://img221.imageshack.us/img221/605/61607025ge8.png I don't see why f(0) = 0 is necessary for E to be a norm. And what does f(0) has to with f being differentible?
  16. M

    Exact definitions of BEC for real gases-liquids?

    While reading papers on various topics in physics i have become very embarrassed with the meaning of such a word as BEC. Even in peer-reviewed papers i can't find any attempt to give exact definition of BEC for real gases. For such topics as: Electron (pair-ed, superfluid) gas, 2D (! do you...
  17. N

    Formal definitions of cutting and pasting etc

    Popular math books usually explain topology as the study of spaces allowing strecthing and shrinking and some cutting and pasting, but what the formal definitions of the intuitive operations "cutting","pasting","strecthing","shrinking" according to mathematics?
  18. lemma28

    Ellipse: geometric equivalence of two definitions

    I've been stuck with this problem: An ellipse can be defined as 1) locus of points for which is constant the sum of the distances from two fixed points (foci) 2) locus of points for which is constant the ratio between the distances from a fixed point (focus) and a fixed line (directrix)...
  19. J

    I used the definitions, now what?

    Homework Statement Prove: 1. R \cap ( S \cup T ) = (R \cap S) \cup (R \cap T) 2. S \cap ( S \cup T ) = S 2. The attempt at a solution I suppose this is all about using the definitions, and I eventually get down to this: For (1), the LHS is down to x e R and (x e S or x e T)...
  20. B

    Mastering Physics Definitions: Tips and Tricks for Effective Memorization

    This probably covers all fields of study in science, but I specifically wanted to know what some of you do to remember or memorize definitions in Physics class? I got some advice to use cue cards and just use them to review every week. Doesn't sound like a bad idea, what do you all think or what...
  21. J

    Yes it's true, but why ? A calculus riddle (of sorts) involving definitions

    "Yes it's true, but why...?" A calculus riddle (of sorts) involving definitions Homework Statement Here's the story: I'm in an AP B/C Calculus class and our current activity is "engaging in an all out study frenzy before the AP exam." We've already gone over all of the material in the book...
  22. T

    Definitions of A & D: Examples & Explanations

    Is there such a definition for A such that A is defined A=>B. Hence nowhere in the definition does it say anything will imply A. Is there such a definition for D such that D is defined C=>D. Hence nowhere in the definition does it specify what D implies. If there exist definitions of A and D...
  23. wolram

    Fair definitions of terrorist and terrorism

    How do you define (terrorist), i have tried to but i am stuck, the only definition i can come up with is, one that kills indiscriminately.
  24. E

    Are Two Definitions of Limit Points the Same?

    Homework Statement I have seen two definitions of limit points. Are they the same: 1)x is a limit point of a set A in X iff each nbhd of x contains a point of A other than x 2) x is a limit point of A if it lies in the closure of A - {x} Homework Equations The Attempt at a...
  25. M

    Definitions of few physics terms

    Hello people, Please, can you help me understand meaning of few definitions like: First, there is so called specific gravity, defined as relative quantity: SG = rho/rho(H2O) at temperature of 4 °C. Since water's density at 4 °C is 1000 kg/m3 = 1 g/cm3, it seems that specific gravity is always...
  26. P

    Are All Math Definitions 'If and Only If' Statements?

    Are all definitions in maths 'if and only if' statement? One book actaully has A=>B as a definition but I should intepret it as A<=>B as the definition?
  27. P

    Exploring Possibilities of Alternative Definitions in Physics

    I've always wondered what would happen if we had different definitions in physics, what theories will come out and would they turn out to be simpler or more elegant then existing ones. Moreoever new definitions may not get us into the quaral that exists in the theory of QM. Anyone else wondered...
  28. murshid_islam

    What is the mathematical logic behind scalar and cross product definitions?

    one of my cousins asked me what the mathematical logic/mathematical explanation are behind the definitions of scalar product and cross product. he wants to know why the definitions are set like the way they are. i just want to make sure from you guys before i answer him. i think that there are...
  29. marcus

    Singularity (Wikipedia and Mathworld definitions)

    This post is just concerned with definition of terms, for them as wants it. If you are NOT confused about what is meant by a singularity in math/physics, please ignore this. Sometimes a good online source, if you want the meaning of math and physics terms, is Wolfram Mathworld. Wolfram also has...
  30. M

    The Difficult Dictionary Definitions Game

    Using a dictionary, pick a world. The more obscure and hard-to-understand the better. Post it. The next person posts the definition of the previous word, a funny comment about it and then a new word. You may consult a dictionary. I'll start: Contumelious
  31. P

    Field trace and norm (Equivalence between definitions)

    I'm sure whoever is familiar with this subject has already seen this several times. I've seen it several times myself, and I even remember proving it in detail a couple of years ago, but now I'm stuck. I'm quoting what my professor did in class. Given some separable extension L/K, say for...
  32. K

    Definitions of Fractional derivative

    how many definitions appart from the 'Riemann-Liouville differintegral' to define the fractional derivative of f(x) or x^{a}f(x) for real or complex 'a' are them all equivalents??
  33. B

    Understanding Pressure: Definitions and Units

    Homework Statement Which of the following definitions or units apply to pressure? True False Newtons per square meter True False kg per cubic meter True False pascals True False force per unit area True False mass per unit volume The Attempt at a Solution My answers are in...
  34. S

    Equivalence betwen diferent definitions of charge

    I am trying to fit together a few definitions of charge which are being commonly used. On one side we have the Noether charge associated with any invariance. Sure most of you know how it goes, you have a Lagrangian invariant under a (Lie) symmetry group and for every group generator (Lie...
  35. D

    Help with definitions in linear algebra

    Having a matrix, how can I know if the function the matrix is representing is: a) Injective b) Bijective Thanks in advance
  36. K

    Aren't all universal statements lexiconically supported definitions?

    Universal statements are not falsifiable. The reason is that they are defined, supported, reliant upon[...] lexicon! Lexicon is not science, but its all about establishing vocal or verbal conventions that are "blurt" whenever referencing some concrete or abstract entity. "All universal...
  37. P

    Measurement Definitions Help

    Homework Statement Fill in the blanks... 1. ___________ indicates how close a measurement comes to its real value 2. the ___________ of a measurement can only be as accurate as the measuring device used. 3. __________ indicates how close a set of measurements are to one another...
  38. W

    Definitions of words and misinterpretation

    So I thought to myself, how about a thread where people would post (just post, not discuss) definitions of words they use that have a lot of room for misinterpretation, such as "intelligence", "consciousness", "matter", "god", etc. Then, whenever a need arises, they could put "(def #153)"...
  39. T

    Definitions using if instead of iff

    definitions using "if" instead of "iff" when a mathematical definition uses the word "if", can we assume that it also means "iff"? for example, here's a defintion straight from a book: definition: a bijection f is a homeomorphism if f and its inverse are continuous. so this definition...
  40. M

    Voltage, Current, Resistance definitions

    Can someone please give a straight forward and easy to understand definition of the 3 mentioned phenomenone in terms of electrons if possible? Thanks!
  41. J

    Understanding the Fundamentals of Charge and Electric Fields

    Hello... I've just recently started studying physics for my A levels and i am finding its concepts very hard to get a handle on :frown: . One major area I am having problems with is my definitions of some of the fundamental properties of electrical circuits. For example i find charge very...
  42. S

    What is the true definition of inertia and where can it be found?

    Lately I've been curious about the very meaning of the most fundamental concepts in physics like inertia. Where do you think is the best place to look for these definitions. Newton's principia?
  43. S

    Complicated definitions of linear independence

    My teacher gave us an intuitive idea of what it means for two vectors in \mathbb{R}^2 to be linearly independent (they aren't multiples of each other) and for three vectors in \mathbb{R}^3 (they aren't on the same plane). Now the book has generalized the idea of linear independence to n...
  44. P

    Momentum, impulse, and power definitions

    Hey, This may seem as stupid query for you people out there, but I would like to know if somebody would be able to spare a moment or two in explaining to me what the terms: momentum impulse power mean/refer to in the study of kinematics. Thank you heaps for your kindness, time and effort...
  45. C

    What is the relationship between mechanics and thermodynamics?

    i want to understand physics as follows 1)Physics is the study of nature 2)mechanics is the study of response of materials(solid & fluid) to the action of forces(changes) 3)mechanics of rigid bodies assumes the material to be rigid is the study of forces acting of solids 4)mechanics...
  46. S

    Are These Definitions of Astronomical Terms Accurate for a Physics Class?

    (not sure if this is the appropriate forum) of astronomical terms for our 'physics of the space environment' class we do not have a textbook... as such looking definitions is hard because we have to formulate or own from teh notes and it may be wrong... ANyway i was wondering if these...
  47. cepheid

    Inconsistent Inner Product Definitions

    Hi, I'm looking at the definition of the inner product of two vectors in \mathbb{C}^n . One source is talking about how the definition of an inner product must be modified to account for vectors with complex components and says: He then goes on to say that we can rewrite conjugate...
  48. S

    How is luminous flux defined and how does it relate to the unit lumen?

    1. What is luminous flux and what is luminous intensity? How are they related? 2. What is the definition of lumen (unit of luminous flux)? How is it related with candela? There are a lot of definitions in my books but I am a bit confused, particularly over the definition of lumen. One...
  49. Ivan Seeking

    Clean words that sound bad or dirty, and alternative definitions

    subduction better yet, add the definition: Subduction is the act of abducting your second choice. Or, as in, "I got subducted on the first date"
  50. S

    Wave Terms: Cycle, Frequency, Resonance, Sympathetic Vibration, Timbre

    I am studying for a test based on concepts and defintions of wave terms. Please help me define the following: Cycle Frequency Resonance Sympathetic vibration Timbre The definitions or a site where I can find many definitions of those terms would be greatly appricated. Thanks.
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