Definitions Definition and 263 Threads

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

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...

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...

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...

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...

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

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...

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

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...

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?

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?

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)...

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)...

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...

"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...

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...

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.

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...

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...

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?

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...

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...

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...

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

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...

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??

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...

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

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...

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...

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)"...

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...

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

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...

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?

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...

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...

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...

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...

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"

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.

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...

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:

What do homogeneity and isotropy mean as properties of the universe? [skippable complaining][/color]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)...

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

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...

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...

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...

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...

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...