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. quantumdude

    Mathematica Mathematical Definitions: If versus Iff

    Mathematical Definitions: "If" versus "Iff" One might expect, perhaps naively, that mathematical definitions should be interpreted as "iff" statements by default, unless stated otherwise. This expectation arises from the facts that a definition expresses an equivalence, and that equivalences...
  2. J

    Epsilon Delta/N Definitions

    I'm have some trouble distinguising definitions and require some help please: is the epsilon-n def. for convergence? is the epsilon-delta def. for continuity? if this is correct could you slighlt elaborate on what it actually means; I'm quite confused and any help would do!:confused:
  3. honestrosewater

    Where are the real definitions of homogeneity and isotropy?

    What do homogeneity and isotropy mean as properties of the universe? [skippable complaining]It seems like a pretty basic question, but I can only find analogies or short and sweet 'definitions' with no context to give them meaning (which aren't necessarily bad - just not helping me). To give...
  4. C

    Exploring Contradictory Definitions of f(M) & F(M) in Press-Schechter Formalism

    In press-Schechter mass formalism what exactly are f(M) and F(M) ? I am finding two contradictiory definitions. In some places it has been said that f(M)dM is the number density of collapsed objects in mass range [M,M+dm] and F(M) is the number density of objects having mass > M...
  5. D

    Generic mathematical definitions of the conics

    Hello, Do you know a website with the most generic mathematical definitions of the conics (parabola, ellipse, hyperbola)? Thanks
  6. A

    Unclear on the definitions

    I know how to solve this type of question, but I don't understand the defintion of a term in it... "Assume that a certain 660-Hz tuning fork can be considered as a harmonic oscillator whose vibrational energy is 0.04 J. Compare the energy quanta of this tuning fork with those of an atomic...
  7. honestrosewater

    Favorite definitions, theorems, proofs, etc.?

    After seeing infinite sets defined negatively, I liked seeing them defined as sets that are equivalent to one of their proper subsets. I always thought diagonal argument[/url] was cool. Do you have a favorite definition, theorem, proof, bit of knowledge you found especially insightful or...
  8. honestrosewater

    Definitions in terms of truth-functions

    In another thread, I started to say that "tautology" and "contradiction" could be defined in terms of truth-functions- which seemed entirely plausible- but I can't figure out how to do it. A tautology is a proposition whose truth-value is always Truth (T); a contradiction is a proposition whose...
  9. B

    Minuend Definition: How Did They Choose the Example Values?

    The dictionary definition of minuend, http://dictionary.reference.com/search?q=minuend includes the equation 50 - 34 = 16 :bugeye: How do they decide which equation to put in there? I mean, the values of 50 and 34, did someone just randomly think of two numbers ? Did they use a...
  10. C

    Definitions of Measurable Functions

    I have seen a number of definitions of measurable functions, particularly, for the following two definitions, are they the same? 1) A function f:X->R is measurable iff for every open subset T of R, the inverse image of T is measurable. 2) A function f:X->R is measurable iff for every Borel set...
  11. C

    Physical quantities and definitions

    Hi everybody, I just want your opinion in some questions: First of all, how do we define a physical quantity? Is it a mathematical creation that helps us describe something happening in nature? And all these formulas that we have come up with: example F=dp/dt . Are they mathematics or...
  12. honestrosewater

    Definitions wanted: Abstract and Concrete

    Pretty straightforward, right? I want some definitions for "abstract" and "concrete". If anyone is interested in doing some reading, here are some links: 1, 2, 3, 4, 5(PDF), http://64.233.187.104/search?q=cache:AUWz3yToePIJ:www.hcrc.ed.ac.uk/cogsci2001/pdf-files/1106.pdf . I see a connection...
  13. quasar987

    A definitions for the terms the limit does not exists

    a definitions for the terms "the limit does not exists" Since my textbook doesn't have a definitions for the terms "the limit does not exists" and "the limit goes to infinity", I tried to make them up. I'd like to know if they're correct. 1) Consider f: \mathcal{D}\longrightarrow \mathbb{R}...
  14. S

    What is the graviton? Please place your definitions

    1. A quantizied gravitational wave... 2. They travel at the speed of light 3. They have never been experimentally proven to exist. 4. They have been theoretically proven? 5. They permeate all dimensions. I have some ideas fixed in my head that need to be corrected. In another thread...
  15. Q

    Your Definitions of Good and Evil

    [as it says above] :devil: <=> :smile:
  16. Q

    Definitions of Science: Share Your Thoughts Here

    What is your definition of science? Have you heard good definitions of science before?...don't be shy... :shy: ... post your thoughts here
  17. H

    Terminology that is inconsistent with basic physic definitions

    When reading advanced physics articles, I frequently find terminology that is inconsistent with basic physics definitions. For example: "pure energy". I have no idea what that expression means. I have read much about space-time, the arrow or time, etc, but no definition of "time". Where...
  18. A

    News Definitions of geo-political terms

    To avoid misunderstandings and mistakes in threads, I thought I would put together this little lot of definitions of geo-political terms. CONTINENTS A continent is a large, unbroken section of Earth's crust above sea level. It is important to specify above sea level, since some huge...
  19. H

    Understanding the Concept of Matter: Definitions and Examples

    Since, we are trying to hold dialogue of some kind, here are some terms, as they are defined by one website: The term Matter: Something that occupies space and can be perceived by one or more senses; a physical body, a physical substance, or the universe as a whole. Physics...
  20. W

    What are the definitions of graph theory and its components?

    Hello, My discrete math course has begun a section on graph theory. And I am hung up on some of the definitions. If someone is familiar with graph theory, I would appreciate it if some of these definitions could be reworded in another way. I will post the definitions we have taken so far and...
  21. L

    What Resource Clarifies Physics Terms Like Kinetic Energy and Momentum?

    Does anybody have a list of all of the different physics definitions, such as Kinetic Energy vs. Velocity, vs. Momentum, vs. Speed or Work vs. Force etc. etc. I tend to get the definitions confused so if there is anybody who has a site or paper which points out the differences between the...
  22. D

    New definitions to the continuum and the discreteness concepts

    p and q are real numbers. If p < q then [p,q] = {x : p <= x <= q} or (p,q] = {x : p < x <= q} or [p,q) = {x : p <= x < q} or (p,q) = {x : p < x < q} . A single-simultaneous-connection is any single real number included in p,q ( = D = Discreteness = a localized...
  23. Ivan Seeking

    Defining Science: Examining Limits & Credibility

    I am going to try for a difficult position here. I intend to question the current definitions of the boundaries of science. Scientists [generically] may violate the scientific method constantly in that many popular assertions made by science may not ever be testable. Cosmologists seem to...
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