Discrete Definition and 897 Threads

1. Show by example that it is possible for g°f(x) to be surjective while f(x) is not I am confused by the general pattern of injectivity (one-to-one) and surjectivity (onto). I know the following by looking through my book: If f and g are surjective, then g°f is surjective. If f is...

Homework Statement Let Z be the set of all integers. Then, S is a relation on the set Z x Z defined by: for (a1, a2), (b1, b2) belong to Z x Z, (a1, a2)S(b1, b2) <-> a1b2 = a2b1. Homework Equations The Attempt at a Solution The actual problem is about symmetry...

Is it possible to have the following signal: 1) Discrete and analog 2) Discrete and digital (I believe this one is true and very common in man made product) 3) Continuous and analog (I believe this one is also true and very common in nature) 4) Continuous and digital If a picture...

Homework Statement Problem from Artin's Algebra, find all discrete subrings of the real set. The Attempt at a Solution Clearly, Zn = {...,-2n,-n,0,n,...} is a portion. But having trouble proving that this forms *all* of the discrete subgroups.

Hi, I'm searching for days for a numerical integration methode for discrete data given at non-equidistant nodes. The simple Simpson rule can only be used for equidistant nodes so I'm looking for methode which I can solve my problem. Any suggestion is welcome! Thanks in advance!

Homework Statement http://s359.photobucket.com/albums/oo40/jsmith613/?action=view&current=MathQUUU.pngHomework Equations The Attempt at a Solution So I know that k = 1 But if F(>3) = 1 then why does F(3) also equal 1 Thanks

Homework Statement For all n ∈ Z+, the function Pn of i variables is defined recursively as follows: Pn(x1,...,xn) = Pn-1(x1 + x2, x2 + x3,...,xn-1 + xn) and P1(x1) = x1. Find a closed formula for Pn. Homework Equations Pn(x1,...,xn) = Pn-1(x1 + x2, x2 + x3,...,xn-1 + xn) and P1(x1)...

We never actually directly detect light, only its interaction with matter. Why do we have to consider this "wave particle duality" with light? Isn't it enough to say that light IS continuous, and it is the discrete nature of mater that gives rise to things like the photoelectric effect? Is...

Homework Statement The question is to provide a new composite heuristic h3 that is admissible and dominates h1 and h2. Then show the cost of each of the states through H according to h3. Homework Equations States: A B C D E F G H h1: 10,12,12,6,7,7,2,10 h2: 8, 9, 14,4,9,7,1,9...

Just wondering how would one design a comparator using just discrete BJTs.

Hi everyone, How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

Hi Guys, I've used this forum as a great resource for a while now and it's always helped me out. Now I'm really stuck on something and was hoping you guys could help out. It's a pretty long question, but if you guys can just give me a general direction of what to do, I can go ahead and work it...

I am starting a maths major and I will going to go into pure maths. I am going to specialize in either analysis or discrete maths. I understand that mathematical analysis has a very strong connection to calculus and that discrete mathematics is used mainly in the cryptography and security...

If I have a large amount of data I can sample, with a several discrete variables, and I need to get an average of some function of that data, but it's too computationally intensive to do exhaustively... I want to do some sampling of the possible outcomes. I guess random sampling (Monte-Carlo...

Homework Statement Is the following a statement: "Next year interest rates will rise" Homework Equations Sort of obvious, but a statement is defined as something which is true or false. The Attempt at a Solution I'm guessing that it is a statement, even if it isn't known whether it...

Hello to everyone :) Since I did not notice a presentation section I put some info about myself before the question,. My name is Enrico, I am Italian (form Modena) and I am 18. I am studying Electronics&Telecommunications in High School and I have applied for UCSD/UCLA/Berkeley (I hope they...

Homework Statement The formulation of the problem confused me a little, so just to check. No T1 space has a locally finite space unless it is discrete. The Attempt at a Solution This means that, if X is a discrete T1 space, it has a locally finite basis, right? Btw, for the...

If I have the unit impulse response function for a discrete-time LTI system (Unit sequence response?), h[n], how can I calculate the time taken for the output to fall below 1% of its initial value, after a unit impulse is applied to the input? In particular, I have: h[n]=(\alpha...

In another forum, I have been challenged to prove mathematically that a certain idea which consists of fields of discrete elements will satisfy http://en.wikipedia.org/wiki/Divergence_theorem" . The fields are not expressible in terms of a differentiable function but rather consist of discrete...

Homework Statement A = {0, 1, 2, 3, 4 ,5} Let R be a binary relation on set A such that: R = {(0,1), (1,0), (1,3), (2,2), 2,1), 2,5), (4,4)} a. Make a Directed Graph for the relation R on A b. What must be added to R to make it reflexive/symmetric?

Homework Statement Consider a discrete-time system, driven by: x[k+1] = Ax[k] for non-zero inital conditions x[0] a) write the closed-form solution of x[k]. If the system is asymptotically stable how should x(k) behave? b) what is condition for asymptotic stability? Homework Equations...

Homework Statement Compute the discrete Fourier transform of the ecg signal, graph the amplitude and phase response. The problem gives data in the form of a ecg.mat file. Contained are two double variables: voltage data for the ecg and a time vector for the ecg. both the voltage and time...

Homework Statement On a long train journey, a statistician is invited by a gambler to play a dice game. The game uses 2 unbiased ordinary dice which the statistician is to throw. If the total score is 12, the statistician is paid 3 dollars by the gambler. However,if both or either dice show a...

First let me pose the assumptions that I am making (because this is not something I am an expert in): 1.) Energy and Mass are equivalent 2.) Quantum mechanics discretizes just about everything, or that a discrete element can be found for everything. 3.) Mass is discrete via the Higgs Boson...

Homework Statement Homework Equations base case: n=1 The Attempt at a Solution im not sure where to start because the examples that my professor showed us did not have a n(n-1) (n+1) but rather (p+1)P=1+1)(2(p+1)+1) im just very lost in this example

Zaki and Ramli play a game in which they take it in turns to toss a tetrahedral dice. They agree that the first man to toss a "2" wins the game. Ramli toesses the dice first. (a) Find the probability that Zaki loses on his first toss. (Ans : 3/16) (b) If x is the probability that Ramli...

Let R be a discrete valuation ring with fraction field F. I believe it's straightforward to show that any torsion-free module M with the property that M \otimes_R F is a finite dimensional F-vector space is of the form R^m \oplus F^n. What if M \otimes_R F is infinite dimensional?

Suppose that the height of adult females in a population is a normal random variable with a mean of 165 cm and a standard deviation of 12 cm. If heights are measured to the nearest centimetre, what percentage of the adult female population will have a measured height between 150 and 160 cm...

Ex 36, p 147. Let f be a function from the set A to the Set B. Let S and T be the subset of A. Show that b) f(S \cap T) \subseteq f(S) \cap f(T). Thanks.

Kempf gave a talk on this. I'll find the PIRSA link. I remember watching the whole video and being impressed. It may be easier to understand than the paper because communicating a higher proportion of the person-to-person intuition---more beginner level. You can try it either way. Either watch...

Hi there, A quick question concerning the FFT. Let's say I explicitly know a 2D function \tilde{f}\left(\xi_1,\xi_2 \right) in the frequency domain. If I want to know the values of f\left(x_1,x_2 \right) in the time domain at some specific times, I can calculate \tilde{f} at N_jdiscrete...

Homework Statement Let \left( X_n \right)_{n \geq 0} be a Markov chain on {0,1,...} with transition probabilities given by: p_{01} = 1, p_{i,i+1} + p_{i,i-1} = 1, p_{i,i+1} = \left(\frac{i+1}{i} \right)^2 p_{i,i-1} Show that if X_0 = 0 then the probability that X_n \geq 1 for all n \geq 1 is...

Discrete Math -- Proof methods Homework Statement Prove |x-y| ≤ |x| + |y| for all real numbers x and y (where |x| represents the absolute value of x, which equals x if x≥0 and equals -x if x<0). prove by cases Homework Equations The Attempt at a Solution

Homework Statement Suppose n > 1 people are positioned in a feld, so that each has a unique nearest neighbour. Suppose further that each person has a ball that is thrown at the nearest neighbour. A survivor is a person that is not hit by a ball. Prove that if n is odd, then there is at least...

Not a specific question per se but... Is it possible to convolve a discrete-time signal with a continuous-time one? if you have x(n) and y(t) can you calculate the convolution of x and y (say, by taking y(t) for t in the set of integers or by treating each x(n) as its value multiplied by...

Homework Statement 1. Suppose u flip a coin Z = 1 if the coin is heads Z = 3 if the coin is tails W = Z^2 + Z a) what is the probability function of Z? b) what is the probability function of W? 2. Let Z ~ Geometric (theta). Compute P(5<=Z<=9). Homework Equations The Attempt at a Solution...

Well, I thought I understood the difference between (weak) convergence in probability, and almost sure convergence. My prof stated that when dealing with discrete probability spaces, both forms of convergence are the same. That is, not only does A.S. convergence imply weak convergence, as...

Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...

Is there any way of proving <p> = 0 for a discrete (bound) state given it's wave function? I've seen proofs using the hermitian properties of p but I'm interested in proving that the integral of Psi*(x) Psi'(x) is identically zero regardless of Psi(x) as long as it's a solution of Schroedinger's...

Do sets in a discrete topological space have boundaries?

Homework Statement I would like to know on how to convert a digital filter transfer function which is in defined in discrete time to continuous time transfer function. Homework Equations The relevant equation is attached...

Homework Statement Prove that at least one of 2*10500 + 15 or 2*10500 + 16 is not a perfect square. Can you say specifically which one is not a perfect square? Consider the proof that √2 is irrational. Could you repeat the same proof for √3? What about √4? Homework Equations n/a...

Homework Statement Which is larger, square root of 2 or cubed root of 3? Prove one is larger than the other without using decimal approximations for either number. The Attempt at a Solution I attempted to solve this through the contradiction that they were even. If they are not even then...

I have solved this problem but still have a question about it (problem and my solution posted below). What I wanted to do was express the problem as a function and use an optimization technique that would require taking the first derivative of the equation. The problem I ran into is: if using...

Quick question: Suppose I have a (transitive) R^n action on a manifold M. If the isotropy group of R^n is discrete, does that mean that it is automatically isomorphic to Z/kZ, with 0<=k<=n? Basically, my discrete subgroup is a lattice then, right? Thanks!

I've been looking over quantum gravity threads here for a year or so. One thing keeps puzzling me. It appears to me that difficulty coming up with a viable quantum gravity theory is melding the continuous nature of the general relativity equations with the discrete (i.e. quantized) nature of...

Homework Statement Let their be a set A, and let B be the set: {A, {A}} (the set containing the elements A and the set that contains element A) As you know, A is an element of B and {A} is also an element of B. Also, {A} is a subset of B and {{A}} is also a subset of B. However...

Which one is a better course to take? I feel like MATLab is simple enough I can learn on my own if I ever need it. How useful is discrete math in physics? Should I take that now or stick to MATLab?

Calculate value(s) of the root(s) of the charateristic equation of a discrete system that correspond(s) to a time constant of 0.03 seconds when the sample period is 0.02 seconds. I'm not sure if I should use a first order or 2nd order equation. Either/or, why is it? Any ideas on how I should...

Homework Statement A random variable X takes values 1,2,...,n with equal probabilities. Determine the expectation, R for X and show that the variance, Q^2 is given by 12Q^2=n^2-1. Hence, find P(|X-R|>Q) in the case n=100 Homework Equations The Attempt at a Solution I can show...