Set Definition and 1000 Threads

Could someone please explain how the image of a set A' ⊆ A is the set: f(A') = {b | b = f(a) for some a ∈ A'}. And how can the complement of A be a subset of A? Forgive my ignorance here, I'm a beginning student of set theory. Edit: Maybe I should rephrase my question: Could you explain what...

Could someone please explain how the image of a set A' ⊆ A is the set: f(A') = {b | b = f(a) for some a ∈ A'}. And how can the complement of A be a subset of A? Forgive my ignorance here, I'm a beginning student of set theory.

Let ##T = \{ \frac{n}{m}\in \mathbb{Q} \vert n, m \in \{ 1, 2, ..., 9 \} \}## No values can repeat (e.g. ##\frac{2}{2},\frac{3}{3},...##) How many elements does the set have. I could just go ahead and count the elements and eliminate the repeats, but I'm wondering if there is a simpler (and...

Hello all, I am currently studying dynamics of a wheel-axle set for my research. My problem is I could not find the same equation for the rate of the change of the momentum in the book, book is a little bit old and I could not find any errata about the book or any other references that...

Homework Statement Find sup A if A = {0.2, 0.22, 0.222, 0.2222, ...} I'll write elements of a set with low case letters and indexes, e.g anThe Attempt at a Solution Begin by definition of supremum: \sup A = a if \forall x \in A, x \leq a and \forall b \in \mathbb R ((\forall x \in A , x \leq b)...

How are you supposed to go about putting together the power set of a set of sets such as X = {{1},{1,2}} What is the power set of X then? And what's the rule for calculating cardinality for the power set of a set that consists of elements which are sets such as the above? Because the set X...

Let $f:R->R$ be a continuous function. Prove that set of points $f$ is differentiable at is a borel set. I need to get to this set by union/intersection of intervals but how? I guess I'm missing a theorem about differentiable points and cotinuity Thanks

Homework Statement Two sources, S1 and S2, send our circular waves that are in phase and of the same frequency. They have the same wavelength (0,5m) and the same amplitude. Will there be a maxima og a minima at the given points: a) S1P = 5.00 m og S2P = 6.50 m? b) S1P = 5.00 m og S2P =...

I am working on a high school science fair project and I wanted to study sonoluminescence. I am having trouble with the setup and I am not sure what kind of stuff I need. I've been referring to websites and papers such as: http://dave.ucsc.edu/physics195/thesis_2010/mccluney_thesis.pdf...

Homework Statement Consider a solid box with dimensions L,W, and H. Let S be the set of all points whose distance is at most 1 from the nearest point inside or on the box. What is the volume of S? Homework Equations Not sure if there are any? The Attempt at a Solution My initial...

Hey gang, I was wondering if there is a non-parametric version of the single set TTest? I know that often people refer to the Wilcoxon signed-rank test, but my understanding is that only tells you about the median, correct? Is there an equivalent that deals strictly with the mean? Cheers!

Homework Statement Suppose R is a relation on A, and define a relation S on P (A) as follows: S = {(X, Y ) ∈ P (A) × P (A) | ∀x ∈ X∃y ∈ Y (xRy)}. For each part, give either a proof or a counterexample to justify your answer. (a) If R is reflexive, must S be reflexive? (b) If R is symmetric...

Hi, So I understand this problem a little, I just can't understand the ending! So saying that we have n elements, we want all the subsets consisting of r elements where r goes from 0 to n. So we want (n choose 0) + (n choose 1) + ... + (n choose n) which is the summation of n choose r for...

Homework Statement Determine the boundary of the following set. As usual, z=(x,y). 0<\left| z-z_0 \right|<2 2. The attempt at a solution The book's solution says "The circle \left| z-z_0 \right|=2 together with the point (0,0)" Why should the answer not be "... together with the...

Homework Statement Let ##E \subset \mathbb R^n## be a measurable set such that ##E=A \cup B## with ##|B|=0## (##B## is a null set). Show that ##A## is measurable. The Attempt at a Solution I know that given ##\epsilon##, there exists a ##\sigma##-elementary set ##H## such that ##E \subset...

I know I can define a sequence on a set ##X## as a function ##a:T\rightarrow{}X##, where ##T## is a countable totally ordered set. But what about series? Can I define a series as a function ##\omega{}:a\rightarrow{}A##, where ##A\in{}X##? Or is this too general to be a series? Do I need to...

Homework Statement Suppose A is a set, and for every family of sets F, if ∪F = A then A ∈ F. Prove that A has exactly one element. (Hint: For both the existence and uniqueness parts of the proof, try proof by contradiction.) Homework Equations The Attempt at a Solution Let A be...

Homework Statement Let U be any set. (a) Prove that for every A ∈ P (U) there is a unique B ∈ P (U) such that for every C ∈ P (U), C \ A = C ∩ B. Remark: P(U) = the Power set of U, i.e. A ∈ P (U) then A⊆U Homework Equations The Attempt at a Solution The question's form is as follows...

"A set in the plane is called a region if it satisfies the following two conditions: 1. Each point of the set is the center of a circle whose entire enterior consists of points of the set. 2. Every two points of the set can be joined by a curve which consists entirely of points of the set."...

how can i find the sets from following situation. i have three numbers,{1 2 3} which will always be in this order {123}, i want to find out number of cases can be made. but 2 can come at frist position that is before 1 or at second position or at third position that is after 3. and all are...

Homework Statement How do we set up a second-order plant transmittance with the only information available are: One pole is at a position where the undamped natural frequency (ωn = 0 rad/sec), and the other pole is at a position where ωn = 2 rad/sec? The question asks to build that...

Homework Statement . Let ##X## be a topological space and let ##A,B \subset X##. Then (1) ##A \cap \overline{B} \subset \overline{A \cap B}## when ##A## is open (2) ##\overline{A} \setminus \overline{B} \subset \overline {A \setminus B}##. The attempt at a solution. In (1), using...

Homework Statement . Let ##X## be a nonempty set and let ##x_0 \in X##. (a) ##\{U \in \mathcal P(X) : x_0 \in U\} \cup \{\emptyset\}## is a topology on ##X##. (b) ##\{U \in \mathcal P(X) : x_0 \not \in U\} \cup \{X\}## is a topology on ##X##. Describe the interior, the closure and the...

I have a group of dogs (3 brown male, 2 brown female, 4 white male, 4 white female, 5 black male, 4 black female) What is the probability to 1. select a female brown dog ? 2. select a female, given that is a brown dog ? 3. select a brown given that is a female dog ? Thank you. I have...

Homework Statement Let b be a symetric bilinear form on V and A = \{ v\in V : b\left(v,v\right)=0\}. Prove that A is not a vector space, unless A = 0 or A = V. 2. The attempt at a solution If we suppose that A is a vector space then for every v,w\in A we must have...

Is there a formula that will give me the equation for the line of best fit of a data set, the line being a 6th degree polynomial? I know how to graph the table and add a line of best fit while showing the equation but as far as I know the equation cannot be used in the given format in excel. If...

i just signed up here so i hope this is the right place. i need to solve a set of 2 non-linear ordinary differencial equations. i tryed using NDSolve but it doesn't really work so I am not sure what's wrong with my code. here is my code (copy paste): c = 0.1; Subscript[sys, B]...

If you take two arbitrary numbers from a set N - let's say N stands for the natural numbers - and add them together, the sum will always be an element of N. In my language, there is a word for this, but i don't know what it is in english? If i translate it from norwegian, it would be something...

Is infinity part of any set?

Let X be an arbitrary set and P(X) the set of all its subsets, prove that if ∀ A,B ∈ P(X) the sets A∩B,A∪B are also ∈ P(X). I really don't know how to get started on this proof but I tried to start with something like this: ∀ m,n ∈ A,B ⇒ m,n ∈ X ⇒ Is this the right way to start on this proof...

I am reading Introduction to Set Theory (Jech & Hrbacek) and in one of the exercises we're asked to prove that the complement of a set is not a set. I get that if it were a set that would imply that "a set of all sets" (the union of the set and its complement, by the axiom of pairing) exists and...

I have very large data sets: coins & amount i.e. {10 & 11, 9 & 7, 8 & 9, 4 & 5, 3 & 1} graphed would show greater volume to the left side while {1 & 0, 2 & 3, 2 & 1, 4 & 6, 9 & 10} would reflect greater volume on the right, and {1 & 4, 2 & 3, 12 & 10, 4 & 4, 3 & 2} would reflect a surge in the...

Hi there, I have a bit of a confusing question, but I'll try to be as clear as I can in asking it. I have a set of linear fits for four different sets of data. Basically, I have three sets of data, with sample sizes N1 = 5, N2 = 7, N3 = 5 respectively. I have plotted these data with...

Hi I am trying to find the equations of a charged particle inside a dipole & quadripole. Practically, I need to write a simulation program for it which assumes a beam passing through a dipole-quadripole-dipole which are setting around an arc. Is there some recommended literature ? Of course...

For those who have read Halmos, in Section 6 Ordered Pairs (page 23 in my book), he gives a non-trivial exercise to find an intrinsic characterization of those sets of subsets of A that correspond to some order in A. I'm curious what that characterization is. A is suppose to be a quadruple...

Hi - Glad to have found this forum. I am looking for a book which contains LOTS of Set Theory word problems with solutions. Anyone aware of a good resource? Thanks in advance.

Homework Statement Theorm 1: If M is a monoid, the set of M* of all units in M is a group using the operation of M, called the group of units of M. My question is this always a "real" group? for example, is this 'group' always closed under the binary operation? Homework Equations...

Homework Statement Prove that the set of all algebraic numbers is a countable set. Solution: Algebraic numbers are solutions to polynomial equations of the form a_0 x^n + a_1 x^(n – 1) + . . . + a_n = 0 where a_0, a_1, . . . , a_n are integers. Let P = |a_0| + |a_1| + . . . + |a_n| + n...

Let B be the non empty sets, B ={(x,y):y = e^x, x belongs to set of real numbers} Write the set in roster form.

Homework Statement (Verbatim) A particle moves with speed .9c along the x'' axis of frame S'', which moves with speed .9c in the positive x'-direction relative to frame S'. Frame S' moves with speed .9c, in the positive x-direction, relative to S. a.) Find the speed of the particle relative to...

I am going through section 14 in chapter 3 in Mary Boas' "Mathematical Methods for the Physical Sciences 3rd ed" Example 1 is clear, but this line is confusing in example 3 (I don't understand why it shows that these are not an element of the set). I have pasted example 1 for reference...

I know that we can easily construct a set whose cardinality is strictly greater than that of the set of real numbers by taking P(\Re) where P denotes the power-set operator. But as far as I am aware there aren't really any uses for this class of sets (up to bijection), or any intuitive ways of...

I am going through James Binney's course on Quantum Mechanics. I love all of the little misconceptions he points out along the way. One thing he mentions in his text and the lectures is found on page 20 and 21 starting with the heading "Commutators" eq. 2.21. He states that non commuting...

Homework Statement For the set S = (-1)^n * (3 + 5/n) I have determined that the maximum is 3 + 5/2 and the minimum is -8. However I am not sure if it is closed; given that it has a maximum and minimum, does this mean by definition that the set will be closed? Homework Equations...

Homework Statement Is {(1; 1; 0);(0; 0; 2);(0; 0; 1);(1; 2; 3)} a spanning set for R3The Attempt at a SolutionThis is supposed to be easy but the answer sheet might be wrong. The answer I have says it is and then proceed to say that (0;0;2) is linearly independent. But it isn't because...

Homework Statement For a set of vectors in R3, is the set of vectors all of whose coordinates are integers a subspace?The Attempt at a Solution I do not exactly understand if I should be looking for a violation or a universal proof. If x,y, z \in Z then x,y,z can be writted as...

I have a problem with this excercise. Ironically I think I can manage the part that is supposed to be hardest, here is the problem: Let (V,||\cdot||), be a normed vector-space. a), Show that if A is a closed subset of V, and C is a compact subset of V, then A+C=\{a+c| a \in A, c \in C\} is...

Hi, I was wondering, how can a null set be a subset of other sets? Could anyone explain the idea in non technical terms, I'm just a beginner. :) Thank you!

Homework Statement 8. Let ##A## be a non-empty subset of ##R## which is bounded above. Define ##B = \{x ∈ R : x − 1 ∈ A\}##, ##C = \{x ∈ R : (x + 1)/2 ∈ A\}.## Prove that sup B = 1 + sup A, sup C = 2 sup A − 1. The attempt at a solution Note that ##sup A## exists. Let ##x ∈ B##; then ##x − 1...

Hi! So let's say we measured the angular momentum squared of a particle, and got the result ##2 \hbar^2##, so ##l=1##. Now we have the choice of obtaining a sharp value of either ##L_z, L_y## or ##L_x##. Okay, fair enough. But I have two questions: 1) The degeneration degree is ##3## because...