Discrete Definition and 829 Threads

Homework Statement I attached the problem as a file. Homework Equations The Attempt at a Solution I get stuck on how to properly represent the summation. How does k find it's way as one of the sub-scripts?

Homework Statement I attached the problem as a fileHomework Equations The Attempt at a Solution The way I tried to solve this was to write out a few multiplications and find a pattern. I got the right answer, but I was wondering if there was more of a precise way of doing it; or would the...

Homework Statement I attached the problem as file. Homework Equations The Attempt at a Solution I honestly do not know how to solve this problem. I have a test tomorrow, and this is really the only question that I am having difficulty with. I don't really know what mod means...

Discrete Math: prove B intersection A = A, given A-B = null set 1. Problem Statement: Prove B \cap A = A, given A-B = ∅ (empty set) The Attempt at a Solution xε(B\capA) => xεB and xεA => Logic given A-B = ∅ => xεA I tried using A-B = A\cap!B for xε(A\cap!B)=∅ => xεA and x not in !B or...

Homework Statement Prove the complementation law in Table 1 by showing that \stackrel{=}{A} = A Homework Equations The Attempt at a Solution Well, first I assumed that x is an element of A, so that A = (x | x\in A) by taking the complement, I got (x | \neg(x\in A)...

Hi everyone, I've got a test tomorrow and while working through a practice test I got stuck. Here is the problem: In the question below suppose P(x,y) is a predicate and the universe for the variables x and y is {1,2,3}. Suppose P(1,3), P(2,1), P(2,2), P(2,3), P(2,3), P(3,1), P(3,2) are...

Feynman checkerboard as a model of discrete space-time Back in 2006 Ed Hanna posted an interesting thread about this topic and I would really like to discuss it with him. Are you out there Ed - or does anyone know how to contact him? Thanks, John Wellings

Homework Statement A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated. What is the probability...

Let A, B, and C be sets. Show that a) (A-B) - C \subseteq A - C b) (B-A) \cup (C-A) = (B \cup C) - A I am using variable x to represent an element. Part A) I rewrote (A-B) - C as (x\inA ^ x\notinB) - C I think this could be rewritten as (x\inA ^ x\notinB) ^ x\notin C A-C can...

The question is, "Find the dual of each of these compound propositions." The propositions being: p∧¬q∧¬r, (p∧q∧r)∨s, and (p∨F)∧(q∨T) I don't quite understand what they want me to do.

Hi all, I have a seemingly simple problem which is I'd like to efficiently evaluate the following sums: Y_k = \sum_{j=0}^{n-1} c_j e^{\frac{i j k \alpha}{n}} for k=0...n-1. Now if \alpha = 2\pi, then this reduces to a standard DFT and I can use a standard FFT library to compute the...

Do you think that matter, energy, space, time, etc. are discrete, or continuous? If they are discrete, is continuous mathematics limited to a very, very good approximation for modeling physical phenomena?

Hi everybody ! I have a question about discrete integrals with contours. I want to integrate the points that makes the contour of an image. When the contour is only one curve it is easy I get the function in every point of the contour and I multiply by the distance between two consecutive...

I'm planning on taking a computer science course this fall on Theory of Computation. However, one of the prereqs is "experience in formal mathematics at the level of [course on Discrete Mathematics]." I've done a little bit of discrete math before (The Art of Problem Solving covers some discrete...

Homework Statement Hello. Here is the question: Determine whether or not R is some sort of order relation on the given set X. X = {∅, {∅}, {{∅}} } and R ε ⊆. I can't seem to figure out why the ordered pairs given are what they are. Homework Equations None. The Attempt at...

is this true or false: If a|b and a|c, then one (or both) of b|c or c|b holds. if I want to disprove this, can I: let a = 5, x = 2 and y = 3. b=ax c=ay then c=bz and c = bg doesn't hold.

I never used descrete math terms in english before, so I hope it sounds clear enough: Formalize the following: 1) Between every two different real numbers there is a rational number 2) There exist real numbers x and y, such that x is smaller than y, yet x^2 is bigger than y^2 Now the solution...

Surely sets with the same cardinality are homeomorphic if we assign both of them the discrete topology. What's preventing us from doing that? For example, (0,1) and (2,3) \cup (4,5) have the same cardinality. With the natural subspace topology they are not homeomorphic - as one is connected...

Homework Statement For any given n, where n is an element of the natural number set, prove n^2 > n +1, for all n > 1. Homework Equations This week in lecture we defined the greater than relationship as: Let S = Natural numbers Let R = {(a,b): \exists c: a = b+c} then aRb The...

Couldn't decide where to post... Chemistry or quantum mechanics... But posted here cause I wanted to know a physicist's view... We know that the electrons in the atom have discrete energy,I mean not just any energy... An electron can't have the energy between 2s and 2p orbitals... But after...

Homework Statement c) Is 'g' a surjective function (onto) ? Justify your answer. Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the...

I apologize for the repost, but I had no replies to my previous post. I figured that I didn't put down a good enough attempt of a solution. I will try to explain what I did in more detail. I have read the rules for the forum, but if I'm still doing something wrong, please tell me. I want to...

Homework Statement Determine the dom(g) Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the entrance requirement : (x;y)...

Homework Statement Question 1 : a) Use Venn diagrams to determine whether or not, for all subnets A,B and C of a universal set U, (A-B) ∪ C = (A∪C) - (A∩B) b) If the statement appears to hold, give a proof, if not, give a counter example. Homework Equations (A-B) ∪...

Question 2: -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations A+D is the set : (Choose only one ) 1. {1, 3}...

Question 1 : -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations Choose the correct option : D - B is the set ...

Hii everyone, I have a sequence {ai,1<= i <=k} where i know the sum of this sequence(say x). I want to know the sum of another sequence {bi, 1<=i <=k}(at least a tight upper bound) where bi=ai*(1/2^i). Or in other words, if you know the sum of the ratio sequence and sum of 1 sequence, how to...

Homework Statement The Question data is as follows : Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 ) Homework Equations Which one of the following statements is true ? 1. The...

Homework Statement Suppose X is a discrete random variable whose probability generating function is G(z) = z^2 * exp(4z-4) Homework Equations No idea The Attempt at a Solution I'm thinking that due to the exponent on the z term, that the exp(4z-4) would be the P[X=3] =...

Homework Statement Let p(x) be a polynomial in F[x]. Show that p1(x)≈p2(x) if and only if p(x)|(p1(x)-p2(x)) is an equivalence relation The Attempt at a Solution To be completely honest, I have no idea where to begin. This class has been a nightmare and this has been, by far, the worst...

Homework Statement For which values of n≥2 does the implication: axb=0 ⇔ a=0 or b=0 For some Zn (n should be a subscript) NOTE: For the a x b, the x should be the x that has a circle around it. I didn't see that symbol in the "quick symbols" :) Homework Equations I know that this...

Hello everyone, I'm a first time poster and I just want to say this forum is great. Every time I have a question Physics Forums is the first site to answer it. So lately I have been really struggling in my Discrete Mathematics I course at my university. This is one of the few times in...

EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.

Hi guys I am new here. I was asked by my professor a problem: a positron-electron pair is produced at the leftmost position of a 1D circular loop of radius R. e+ moves along the bottom hemisphere and e- moves along the upper one. They are confined in the circular loop and perform circular...

Would learning discrete math be more beneficial then diving into velleman's book right away? and what is a good book on discrete math?

Would Newton's method or some other method work? Consider the following problem: find the zeroes of the function: y = 40sin(2x) - floor(40sin(2x)) where Y,X \in R I don't exactly know how to handle this problem. My best insight so far is that it is only equal to zero whenever 40sin(2x)...

Hello all, I'm aware of the Monte Carlo Summation method in discrete spaces, where you can approximate a very long summation over the entire space by a shorter one with only a few randomly selected terms from the original summation (weighted by the inverse probability density of them being...

Homework Statement show that for positive r and s, with r<s, we always have: r<(r+s)/2<s and 2/[(1/r)+(1/s)]^2< 2rs< (r+s)^2 Homework Equations The Attempt at a Solution i have shown that r<s because r+r<s+r, 2r<s+r, r<(s+r)/2 and 2r< (2s+2r)/4 (r+s)^2= r^2+2rs+s^2...

Homework Statement Suppose that a menu consists of 4 main dishes, 9 choices of side dishes, and 6 desserts. A small meal consists of one main dish and two different side dishes and no dessert. A large meal consists of one main dish, two different side dishes and dessert. How many patrons must...

I have seen the following "extension" of discrete random variables definition, from: pediaview.com/openpedia/Probability_distributions (Abstract) "... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...

About the definition of "discrete random variable" Hogg and Craig stated that a discrete random variable takes on at most a finite number of values in every finite interval (“Introduction to Mathematical Statistics”, McMillan 3rd Ed, 1970, page 22). This is in contrast with the assumption that...

Came across this video which says that a moving object has to cover infinitely many intervals in order to get from one point to another and because of this motion couldn't really take place and since it does take place, its a paradox. youtube.com/watch?v=u42Y3RbP7JE Since motion does take...

Homework Statement This question has two parts: a) How many integers are there between 100 and 1,000,000 with the property that the sum of their digits is equal to 6? b) How many integers are there between 100 and 1,000,000 with the property that the sum of their digits is less than 6...

Homework Statement Find the general solution to the following recurrence relations (defined n≥2). c) an=6an-1-9an-2+8n+4 Homework Equations The Attempt at a Solution an=6an-1-9an-2+8n+4 8n+4= an -6an-1+9an-2 R2-6R+9=0 R=3,3 So hn=A(3)n+B(3)n Assume pn=Cn+Cn2 → This is where I got...

I was having a conversation with my brother, a mechanical engineer, about Digital Signals processing. I was trying to explain what I had recently done in my digital controls class, and how we would use the state space model \vec{x}(k+1) = {\bf{A_d}}\vec{x}(k) + {\bf{B_d}}u(k) in discrete time...

A) Let us say that we have some arbitrary sequence of natural numbers. e.g. 1, 2, 7, 3, 17, 19. Is it possible to convert every finite and infinite sequence into some continuous function model, such as in Fourier theory? I know that it is possible to extract some discrete samples from a...

Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity. But if i recall correctly from complex...

Hi there, I have a short thought that I want to share with all of you and see if there has been something written about it and, if not, why not?: A free particle spin is something that can take a discrete range of values, as it happens with electromagnetic or colour charge. However the other...

Homework Statement Compute P(X=k l X+Y=p)Homework Equations The Attempt at a Solution No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the...

Homework Statement X1 and X2 are two independent discrete random variables with P(X1 = k) = c3-k P(X2 = k) = d4-k for k in natural numbers and where X1, X2 in natural numbers is almost always valid. 0 is not include in N. Find constants c and d. Homework Equations The Attempt...