Discrete Definition and 829 Threads

We know that every discrete metric space with at least 2 points is totally disconnected. Yet I read this: A MS that is countable with more than 2 pts is disconnected. Is it that I'm misreading this statement. It sounds like if it has 2 or less points it is connected? more means greater than.

Hi guys! I got really stuck with a Discrete Mathematics homework in Integers and Algorithms. I know it is not very clear due to lack of symbols. If anyone didn't understand some part of the exercise I would like to clarify it. The exercise is the following : Homework Statement Define for B...

This is a question i hope someone on the forum can help me answer. Recently In a lab i had this question pop into my head, here goes: If I have a set of data and i am asked to find the derivative, I can plot it using the equation f'(x) ~ (y2-y1)/(x2-x1) if i have sufficently close points. A...

hi, i have trouble in understanding the concepts of the impulse response first of all, let's assume that we have a signal y[n] = x[n] which is time invariant and linear, hence if I understand correctly linear means that if for input a*x1[n] we have an output a*y1[n] b*x2[n] we...

Hi... It is an easy to see fact that, instead of moving along the hypotenuse of a right triangle, one starts from the lower corner and reach the upper corner moving only along the directions of the other two sides, i.e only vertically and horizontally and not diagonally...the distance moved...

Homework Statement Define the relation a I b ( a divides b) between integers a and b and then define the greatest common divisor, gcd ( a,b), and the lowest common multiple, lcm ( a,b) Is there any number for m for which you have n I m ( n divides by m) for every n. I just found this...

Hi All, I've come across a theorem that I'm trying to prove, which states that: The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete.. To a lesser extent I'm also interested in the H...

Homework Statement Let A be the set of all strings of a's and b's of length 4. Define a relation R on A as follows. For all s,t \in A, sRt, s has the same first two characters as t. s=baaa t=abaa Homework Equations The Attempt at a Solution I just want to know if the order of the first two...

Homework Statement How many was can 3 identical prizes be awarded to 98 potential winners? Homework Equations The Attempt at a Solution Well. I know that if the prizes were unique, the first prize would have 98 possible winners, the second prize would have 97 possible winners...

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...

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 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...

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 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!