# 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.

View More On Wikipedia.org
1. ### I About the use of nominal definitions in physics

Hi, I was reading the interesting lecture of Feynman about Characteristics of Force -- https://www.feynmanlectures.caltech.edu/I_12.html He basically says that nominal definitions like mathematical definitions of "abstract" objects have actually no physical meaning. For instance take the...
2. ### Is there a word for this? The means become the end...

Is there a word for when when the purpose of some activity is forgotten, and the activity is confused as an end in itself. The means becomes the end? Examples: You need a ladder, so you cut down a tree to make one. Then remember that the reason you wanted the ladder was to climb the tree...
3. ### I So what are the definitions of gas, liquid, solid?

Obviously, we know intuitively what they mean, but it seems that physicists have developed an objective definition for all of these. If I were to guess, I'd say that: - a gas is vastly less compressible than a liquid or solid (i.e., which are considered in thermodynamics as basically...
4. ### B Questions about Feynman's contrasting Definitions and Laws in physics

https://www.feynmanlectures.caltech.edu/I_10.html (From the paragraphs after equation 10.5) 'It is not just a definition to say the masses are equal when the velocities are equal, because to say the masses are equal is to imply the mathematical laws of equality, which in turn makes a prediction...
5. ### Problem understanding entropy (two different definitions?)

In the definition of entropy, there are two. One is about the degree of randomness and one is about energy that is not available to do work. What is the relationship between them?
6. ### I Are Newton's Laws just definitions?

I have read a bunch of articles online regarding my question, and none have helped. Newton's Laws: 1. In an inertial reference frame, an object's momentum doesn't change unless acted upon by a force. 2. In an inertial reference frame, the force on an object equals the time derivative of its...
7. ### B Electric flux -- Which of these three definitions is correct?

I have read three definitions of electric flux in textbook which is confusing me.. 1. Electric flux is the number of electric lines passing through any area of a surface. 2. Electric flux is the number of electric lines passing through unit area per second held perpendicularly. 3. Electric flux...
8. ### Connection between the two definitions of entropy

Hi All, I would like to know how can one connect the two definitions of entropy ##\Delta S = \int_{T_i}^{T_f} \frac{dQ}{T} ## and ##\Delta S = k_B \ln (\frac{W_f}{W_i})##, particularly I am interested in how the logarithm emerges. Does it have to do with some linear dependence of the heat with...
9. ### Two definitions of material dissipation factor

Hi, I have seen two versions of definitions of material dissipation factor Df: The first one: Dk (dielectric constant) = K = relative permittivity = ɛ -jɛ’ , ɛ = energy stored and ɛ’ = energy lost. Df (dissipation factor/loss tangent) = ratio of ɛ’ and ɛ The second one: On slide 8 of webinar...
10. T

### B Giving definitions, proposing theorems in abstract spaces

Hello. Questions: how to give new definitions of things in abstract spaces?What are the criteria? Is it just acceptable to define things that do not contradict with other things on the abstract space?What are the motivations to give definitions of things?Also, what are the motivations for...
11. ### B Are proofs needed for definitions? Conditional probabilities

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P} appeared and it's just not sitting right with me. I know that...
12. ### Should definitions of future computer languages incorporate IDE technologies?

The definitions of currently popular computer languages assume only the technology of printing. For example, they provide syntax for printed expressions in one location that refer to printed expressions in other locations (e.g. "include" type syntax ). However, they don't assume that such...
13. ### Pre 2019 definitions for an Ampere, how is this useful in practice?

I've been looking into definitions for SI units (pre 2019) I'm fine with length based on a certain transition of a Krypton atom and the wavelength associated with it, a spectrometer can be used to find the wavelength of the spectral line and then multiply up... but with the ampere, the idea of...
14. ### What is an inertial frame? A conflict of two definitions

Good Morning (I see this has been discussed here, but I am more interested in two specific definitions and whether the conflict.) I had always thought that the definition of an inertial frame was: "A frame in which Newton's Laws are valid." A person has been arguing with me that the definition...
15. ### I Equivalence of two different definitions of quasicrystals

https://en.wikipedia.org/wiki/Riemann_hypothesis#Quasicrystals a quasicrystal as "a distribution with discrete support whose Fourier transform also has discrete support." https://en.wikipedia.org/wiki/Quasicrystal#Mathematicsdefines a quasicrystal as "a structure that is ordered but not...
16. ### I Local Basis in Topology .... Definitions by Croom and Singh .... ....

Fred H. Croom (Principles of Topology) and Tej Bahadur Singh (Elements of Topology) define local basis (apparently) slightly differently ... Croom's definition reads as follows:... and Singh's definition reads as follows: The two definitions appear different ... ... Croom requires that each...
17. ### I Definitions of Continuity in Topological Spaces ....

I am reading Wilson A. Sutherland's book: "Introduction to Metric & Topological Spaces" (Second Edition) ... I am currently focused on Chapter 8: Continuity in Topological Spaces; bases ... I need some help in order to prove Definition 8.1 is essentially equivalent to Definition 8.2 ... ...
18. ### I Alternative Definitions of the Epsilon-Delta

Formal definition (epsilon-delta definition) of limit is symbolically as follows: $$\lim_{x \to c}f(x) = L \iff [\forall \epsilon > 0,\ \exists \delta > 0,\ \forall x \in I,\ (0 < |x - c| < \delta \implies |f(x) - L| < \epsilon)]$$ Now I want to create alternative definitions out of this by...
19. ### How to characterize mathematical models for comparison

I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do...
20. ### I Mathematic Definitions and Ideas

What is opposite in Mathematics? I argued with my engineering brother and his pal that "inverse" is indeed "opposite" if you use the general concept of "opposite." My brother claims that the idea of opposite in mathematics only means returning to null. Opposite: 1.) Having a position on the...
21. ### MHB Carothers' Definitions: Neighborhoods, Open Sets, and Open Balls

The Definition of a Neighborhood and the Definition of an Open Set ... Carothers, Chapters 3 & 4 ... I am reading N. L. Carothers' book: "Real Analysis". ... ... I am focused on Chapter 3: Metrics and Norms and Chapter 4: Open Sets and Closed Sets ... ... I need help with an aspect of...
22. ### I Planck had 2 definitions of energy in 1900, how?

So, I was looking into Einstein's 1907 paper where he derived the specific heat of solids using quantum mechanics and I found that Einstein just took the derivative of Planck's equation from 1900 for the average energy, U, as a function of time (and multiplied it by 3N for the three dimensions)...
23. ### A Definitions of Cylinder Sets and Cylinder Set Measure

I'm trying to learn about Abstract Wiener Spaces and Gaussian Measures in a general context. For that I'm reading the paper Abstract Wiener Spaces by Leonard Gross, which seems to be where these things were first presented. Now, I'm having a hard time to grasp the idea/motivation behind the...
24. ### B Finite & Infinite: Univerally Accepted Definitions?

I'm troubled by what I think the 'community' considers them to be, but I'm not sure if I'm correct. It appears as though finite is thought to have both an end and a beginning, but is it true that infinite (infinity) is thought to only have no end? Is this accurate? If so, then it would seem like...
25. ### A Equivalence of diffeomorphism definitions

Hi Lets start off with the definition of diffeomorphism from Wolfram MathWorld: The issue is that I am learning about smooth manifolds, and in the books I've read, the map has to be smooth and have a smooth inverse. Also, the definition above doesn't say that it has to be bijective. However...
26. ### Transmission Line Coefficients & Definitions

Homework Statement (a) State what is meant by a ‘distortionless’ and a ‘lossless’ transmission line.(b) A transmission line has the primary coefficients as given below. Determine the line’s secondary coefficients Zo, α and β at a frequency of 1 GHz. R = 2 Ω/m L = 8 nH/m G=0.5 mS/m C=0.23...
27. ### Understanding Constitutive Definitions in Cont. Mech.: What Does It Mean?

while I study in cont. mech. I found this equation and in the index he mention that "the difference between the volume supply and the production phi can be recognized only in relation to the constitutive definition of the material" what does it mean?
28. ### Understanding the Work-Energy Theorem

Are the following definitions correct? Work done as energy transferred The energy transferred when the forces between two objects interact Work done by a force Work done = force x distance moved in the direction of force applied (W=F*Δs) Work done by a gas Work done = pressure x change...
29. ### I Cartesian Product Definitions

I was studying Group Theory on my own from a mathematics journal and got confused at some point where it defines Cartesian products, from binary one, say (A × B), to n-tuples one, say (A_1 × A_2 × ... × A_n). What confuses me when I tried to read it is that the definition made for infinite...
30. ### I Integrals: Math & QM Definitions

Math definition: integral of function within limits divided by difference of limits. QM definition: integral of complex conjugate of wave equation times function times wave equation within limits of minus to plus infinity.

49. ### Electrical charge, current definitions

What is electrical charge? is it a measure of the abundance of electrons within a system? Current is defined as the amount of charge flowing between any two points in a system over a given period of time, correct? but what is elctrical charge if possible to define it better/further. I am...
50. ### B Discrete definitions of Physics Standard Units

Dear PF Forum, Perhaps it's not a question, just a light discussion. Time From this, we get the standard time https://en.wikipedia.org/wiki/Caesium_standard, it's 9,192,631,770 ticks per second. I think this number should be discreet. No need to tune it to some figures after decimal point. Is...