Discrete Definition and 829 Threads

I was wondering what the majority opinion was on this issue, among physicists and philosophers as well. I can't imagine zooming in a million times smaller than the plank length and still not being at a smallest length, however a discrete universe doesn't make much sense to me. Are there any...

I've been having trouble finding many pure math Ph.D. programs with active research groups in the general field of discrete mathematics (perhaps due to its interdisciplinary nature). I'm only aware of the top schools in this field (e.g. Carnegie Mellon, Georgia Tech, UCSD, Rutgers); can anyone...

Homework Statement let d be a metric on an infinite set m. Prove that there is an open set u in m such that both u amd its complements are infinite. Homework Equations If d is not a discrete metric, and M is an infinite set (uncountble), then we can always form an denumerable subset...

Homework Statement Prove the second absorption law from Table 1 by showing that if A and B are sets, then A ∩ (A ∪ B) = A. Homework Equations Absorption laws A ∪ (A ∩ B) = A A ∩ (A ∪ B) = A The Attempt at a Solution i will show A ∩ (A ∪ B) is a subset of A x is any element in A...

These are potential proofs for the discrete math exam on Tuesday. I haven't been able to find proofs online. I have senioritis, and I'm graduating in a few weeks. Is a proof by contraposition the best way to prove this? If you assume h is not a function or g is not a function, then that would...

Hi Guys, Long time reader first time poster... This simple question has stumped me all day and I think I've finally cracked it! I'm hoping someone can confirm that, or tell me how wrong I am - either is fine :) One in 1000 cows have a rare genetic disease. The disease is not contagious...

I'm confused about the DFT of the data, fn = cos(3\pin/N) for n=0,1,...,N. It is definitely an even function, and I read that the Fourier coefficients of an even function is real. But when I take the FFT of this in Matlab I get complex numbers, not real numbers. What am I missing? Thanks ...

Homework Statement I have a whole two courseworks on Genetic Algorithms, but we have been shown no examples. I am stumped! 1. A function f is set to depend on five variables x1, . . . , x5 where x1 can take 2 different values, x2 can take 8 different values and x3, x4, x5 each take 4 different...

Edit: I have to think more about this, I'll post later.

For some questions strong induction would test for cases n+1, n+2 and for other n+1,n+2,n+3, or other ways, why is that? Here's two examples Suppose that the only paper money consists of 3-dollar bills and 10-dollar bills. Find what dollar amounts can be made from a combination of these...

Hello, I'm currently in high school and going over discrete uniform distribution, and we've come across this formula. I'm curious if anyone could show me how the formula is true, as when I asked my teacher he just said that it'll confuse the class and we don't need to know why it's true. If...

Homework Statement Prove that if k>1 then, 5/(k-1)-3/k-2/(k+2) = (9k+6)/(k-1)k(k+2) Hence simplify Ʃ of k=2 to n {(3k+2)/(k-1)k(k+2)} Homework Equations The Attempt at a Solution Ok so the first part is ok I just multiplied the denominators with the numerators and...

I read the definition of discrete math and i read the definition of discrete. i just can't seem to figure out what discrete math is, can you guys show what it means?

Hello all, first time here and I have really silly problem... I am working on something in MATLAB, in which I have to make discrete Fourier transform of gaussian distributed variable. i.e. array of numbers which are taken from f(x)~exp(-x^2). I know that when you Fourier transform it with...

Homework Statement Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not logically equivalent. Homework Equations a → b = \nega v b The Attempt at a Solution I'm sorry. I'm completely stumped on how to go about this problem. I'm not asking for the solution since I want to know how...

Homework Statement If s (0,1), find |P(S)|, |P(P(S))|, |P(P(P(S)))| Homework Equations The Attempt at a Solution |P(S)| = {(0), (1), (0,1), ∅} = 4 |P(P(S))| = {...} = 16. |P (P(P(S)))| = {...} = 16 ^4 ...but how? as my lecturer explained it, it come from pascals...

(3) Define a function A(m,n) as follows. A(0,n) = 2n for every n. A(m,0) = 0 for every m >= 1 A(m,n) = 2 if m >= 1 and n = 1 A(m,n) = A(m -1,A(m, n - 1)) otherwise (i.e., if m >= 1 and n >= 2. (b) Prove A(m,2) = 4 for every m >= 2 (c) Prove A(1, n) = 2^n for every n >= 1. Proving...

Verify that an exact solution exist for the logistic difference equation $$ u_{t+1}=ru_t(1-u_t),\quad r>0 $$ in the form $u_t=A\sin^2(\alpha^t)$ by determining values of r, A and alpha. Is the solution periodic? Oscillatory? I have yet to encounter a problem that says verify a solution...

I have a set of N data points defined over a periodic interval, 0\le x \le 1. I made a discrete fast Fourier transform of these data points and I get a discretized function in the Fuorier space. My question is what are the coordinate of these data points in the Fourier space? I mean, in the real...

The book works out the case with x and y irrational and xy rational. They used the nonconstructive existence proof method with x = sqrt(2) and y = sqrt(2). If that's rational, then you're finished. If it's irrational, then you can simply raise it to the power of sqrt(2) to get 2. I'm not sure...

"For the router to support the new address space it is necessary that the latest software release be installed." I said Q: The latest software released be installed R: The router to support the new address space. I interpreted this as Q is necessary for R, therefore R => Q. The professor has...

Homework Statement Use the equivalence p\rightarrow(r \rightarrow s) \equiv p\wedge r\rightarrow s to rewrite the following problem before the proof. Homework Equations [p\rightarrow (q\rightarrow r)]\wedge (p\rightarrow q) \tautologicallyimplies (p\rightarrow r) The Attempt at a...

The population of a certain species subjected to a specific kind of predation is modeled by the difference equation $$ u_{t+1}=\frac{au_t^2}{b^2+u_t^2}, \quad a>0. $$ Determine the equilibria and show that if $a^2 > 4b^2$ it is possible for the populationto be driven to extinction if it...

So the book is showing an example about discrete steady states but neglected to show how the steady states were found. Here is what it has $u_{t+1}=ru_{t}(1-u_t), \quad r>0$ where we assume $0<r<1$ and we are interested in solutions $u_t>0$ Then it list the steady states $u^*=0, \quad...

Here's the problem. Theorem: If n^2+1 is odd, then n is even. Give indirect proof.

How to solve log10000000 base is 10.

How to solve log100000000, base is 10.

What if: There are only discrete protons in the atomic nucleus combined with electrons (not the orbital ones) being shared,in some random manner, leaving a net positive charge. The two particles only become discrete with the known different characteristics when the atom is "smashed" and a...

Q 1. On a circular island we build n straight dams going from Sea to sea, so the ever two intersect but no three go through the same point. Use Euler’s Formula to determine how many Q 2. Into how many parts do two quadrilaterals divide the plane, If (a) They are convex (b) They are not...

I am currently a CS undergrad. my university offers no courses in Abstract algebra or Number theory or Topology or Analysis. recently I have got interested in Number theory in Discrete math course. moreover I was and still am interested in algebra too. but the problem is, can I apply to CS grad...

Hi guys, Long time lurker of this forum, but first time poster. Discrete Math is going to be the end of me; I'm just not understanding how to solve problems and write the proofs. Any help would be greatly appreciated. Thanks in advance. The Problem: Let nεZ≥1. Show that...

Prove that (A n B) - C = (A - C) n (B - C). n = intersect ≠ε = not a member I got the first one by doing: (xεA ^xεB) ^X≠εC ( by identity law and compliment law) where would I go on from now?

Ceiling = "{" & "}" Floor = "[" & "]" f(X) = [ 1/2 - {x/3}] How would I graph this function? Note: If the decimal is floors it will be rounded down , if the decimal is ceiling it will be rounded up. ~Thanks.

Hello Forum, a continuous time, continuous amplitude sinusoid like sin(2pi*f*t) is 2pi periodic: sin(2pi*f*t)=sin(2pi*f*t+m*2pi) where m can be any positive or negative integer. Let's sample the sinusoid at a sampling frequency fs (sample interval is ts=1/fs) and get the discrete signal...

the discrete time system defined by y[n]= x[n] ^ 2 Is it time varying ? I proceeded as follows x[n] → x[n]^2 x[n+a] → x[n+a]^2 so y[n+a] = x[n+a]^2 So according to me it is time invariant Am i right ?

Homework Statement Find all subrings of \mathbb{R} which are discrete subsets Homework Equations For the purpose of our class, a ring is a ring with identity, not necessarily commutative. The Attempt at a Solution First suppose that S\subset \mathbb{R} is a subring of \mathbb{R}...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Hi, Suppose we have these two functions and their z-transforms are P(r,z)=\sum_{t=0}^{\infty}P(r,t)z^t and F(r,z)=\sum_{t=0}^{\infty}F(r,t)z^t. Now we are going to transform the following convolution of P and F: \sum_{t'\le{t}}F(r,t')P(0,t-t'). The result is said to be F(r,z)P(0,z). But I don't...

I want to do a discrete Fourier transform of the solution I have found using NDSolve, however, because the NDSolve creates Interpolating functions rather than numbers I can't do this. Any help is appreciated. I've attatched the file I'm working with. Catrin

String field from Loop SpinfoamQG:how to build SM matter on discrete quantum geometry note: EPRL is the current standard spinfoam formulation of Loop Quantum Gravity. http://arxiv.org/abs/1201.0525 String Field Theory from Quantum Gravity Louis Crane (Submitted on 2 Jan 2012) Recent work...

Hi, I need help in proving the equation in the attachment. Thanks darkfeffy

Hi all, I am currently doing my Final Year Project on the topic of Optimal Placement of Suicide Bomber Detectors. Given 2 dependent bomb detectors, I am trying to prove that the probability of detection in the intersected area will be larger than the individually covered areas, by working...

Hi, I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables. This would be easy if they were independent, but they’re not. There is a known correlation between...

Homework Statement Let the DTFT (Discrete time Fourier transform) of a signal beY(f)= {1 0≤lfl< \frac{fs}{8} {0 OtherwiseCalc y(k) Homework Equations y(k)=\frac{1}{f_{s}}\int Y(f) e^{jk2\pi fT}df lkl≥0 The Attempt at a Solution So what I understand from this is that my Y(f) is basically 1...

Did this as a homework problem, got it wrong obviously. Not too sure how to solve it otherwise Homework Statement Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+N) Homework Equations The Attempt at a Solution f^(m+1) f^(n+1) = f(f^m) * f(f^n) =...

Hi. I wanted to know in what way the group of translations on a real line with discrete topology (let's call it Td) will be different from the group of translations on a real line with the usual topology (lets call it Tu)? Is Td a Lie Group? Will it have the same generator as Tu?

Homework Statement Figure out a self-referential formula for the number of handshakes required for a group of n aliens to introduce themselves by hand-calculating a few small values and coming up with a solution. Homework Equations We are given: Let H(n) be the number of handshakes...

I know that an atom "absorbs" a particular frequency of energy depending on which element and which electron in this element. The question is (for example) if we take one known emission frequency from a particular element, and use that exclusively to bombard another element for a lower...

Homework Statement Question 1: a) Suppose you have brought four pens of different colours to the exam. For each of the ten question on the exam, you choose one pen. In how many ways can this be done? b) In how many ways can you distribute six bananas and five oranges between three children...

Homework Statement Using contradiction, prove that for every four positive real numbers c, d, e and f, at least one of c, d, e, f is greater than or equal to the average of c, d, e, f. Homework Equations I don't believe that there are any relevant equations for this problem. I do know that...