What is Set: Definition and 1000 Discussions

Seth, in Judaism, Christianity, Mandaeism, Sethianism, and Islam, was the third son of Adam and Eve and brother of Cain and Abel, their only other child mentioned by name in the Hebrew Bible. According to Genesis 4:25, Seth was born after Abel's murder by Cain, and Eve believed that God had appointed him as a replacement for Abel.

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  1. pellman

    I Why is the Axiom of Power Set needed?

    In the Zermelo-Fraenkel axioms of axiomatic set theory we find: Axiom. Given any set x, there is a set such that, given any set z, this set z is a member of if and only if every element of z is also an element of x. Why is this needed as an axiom? why isn't it merely a definition? Under...
  2. dRic2

    Help understanding an experiment set up

    Hi, I'm reading a paper about combustion and I can't understand the composition of the inlet mixture. Here's what the paper says: "A known flow rate of the isobutene (Matheson, TriGas, 99.5%) in nitrogen (General Air, 99.998%) was introduced into a 6mm ID quartz reactor that was heated in an...
  3. S

    I Commuting set of operators (misunderstanding)

    I don’t see how the definition of |an> transmorphs into the statement involving the kroneck delta functions.
  4. G

    Calculate polarization energy over a set of cuboids

    Dear Physics Forums members, I have a research problem that involves electrostatics. My education is as a chemist, and thus I struggle to accurately represent my problem, so I thought that you guys could help me (and would be interested in the exercise). Here is an image to summarize my...
  5. T

    Distance of a point from a compact set in ##\Bbb{R}##

    Homework Statement Let ##K\neq\emptyset## be a compact set in ##\Bbb{R}## and let ##c\in\Bbb{R}##. Then ##\exists a\in K## such that ##\vert c-a\vert=\inf\{\vert c-x\vert : x\in K\}##. 2. Relevant results Any set ##K## is compact in ##\Bbb{R}## if and only if every sequence in ##K## has a...
  6. Mr Davis 97

    I Using group action to prove a set is a subgroup

    Problem: Let ##G=S_n##, fix ##i \in \{1,2, \dots, n \}## and let ##G_i = \{ \sigma \in G ~|~ \sigma (i) = i \}##. Use group actions to prove that ##G_i## is a subgroup of G. Find ##|G_i|##. So here is what I did. Let ##A = \{1,2, \dots, n \}##. I claim that ##G## acts on ##A## by the group...
  7. karush

    MHB La1.1.22 3 aug matrices for linear sys solution set is x_1=3,x_2=-2,x_3=-1

    $$\tiny{la1.1.22}$$ $\textsf{Construct 3 different augmented matrices for linear systems whose solution set is}$ $$x_1=3,\quad x_2=-2,\quad x_3=-1$$Well we could start just by$$3x-2y+y=-1$$but then we need a $3\times4$ matrix
  8. S

    I What is the term for a set of loci that are the same?

    I'm thinking the term is congruent. For example, let's say there are 2 parametric lines: s0( t ) = < 2 , 1 > t + < 0 , - 3 > s1( t ) = < -18 , -9 > t + < -6 , -6 > The loci for both are the same line, just that one proceeds in the opposite as the other (and at a high rate) per change...
  9. U

    How to calculate triac angle to set desired RMS voltage

    Hi, I would like to implement voltage regulator based on microcontroller + triac. I am able to calculate source RMS voltage by sampling signal using ADC, but don't know how to calculate triac angle to set desired RMS voltage. For example i have 250v source RMS voltage and i need to calculate...
  10. C

    MHB Having difficulty finding the elements in each set

    Find the elements in each set given that: U={1,2,3,4,5,6,7} A={1,3,5,7} B={2,4,6} C={1,2,5,6} D={2,3,4} A) C intersect D B) C-D C) (A union B) union C D) (C union A)' -D
  11. S

    Every subset of a finite set is finite

    Homework Statement Proposition. Every subset of a finite set is finite. 2. Relevant definitions Definition. Two sets ##X## and ##Y## have the same cardinality iff there is a bijection between ##X## and ##Y##. A set ##X## is finite iff there is a bijection between ##X## and ##\{1, ... , n\}##...
  12. F

    MHB Choose from the following set of vectors in R4

    Hi everybody, I have a problem with this question: Choose from the following set of vectors in R4 set of the maximum number of linearly independent vectors: 1.(1;2;3;4) 2.(2;4;6;8) 3.(0;1;-1;1) 4.(1;1;1;0) 5.(0;3;0;0) So, I can find a rank of a matrix, it's 4, but I can't understand how it...
  13. Mathmellow

    MHB Proving that a subset of a countable set is countable

    I am trying to prove that any subset of a countable set is either finite or countable. I know that a set S is countable if there exists a bijection that takes S to \Bbb{N}. My first thought was to consider the subset V of S. If V is finite we are done, since we can always construct a finite...
  14. V

    MHB Does limit of "approximate zero set" converge to the zero set?

    Let f:\mathbb{R}^m\rightarrow\mathbb{R}^m. Define the zero set by \mathcal{Z}\triangleq\{x\in\mathbb{R}^m | f(x)=\mathbf{0}\} and an \epsilon-approximation of this set by \mathcal{Z}_\epsilon\triangleq\{x\in\mathbb{R}^m|~||f(x)||\leq\epsilon\} for some \epsilon>0. Clearly \mathcal{Z}\subseteq...
  15. J

    Observed battery set discharge unbalance

    I previously posted the below as a footnote on one my posts on the Mechanical Engineering Forum and it was suggested I start this thread on the subject here. "PS On a general note about battery replacements. On my field GPS I use rechargeable batteries and always test them before recharging...
  16. T

    Solving a set of nonlinear quadratic equations

    I would like to solve this system, which is a sets of non linear quadratic equations, the system needed to be solved can be expressed in general as follow: ϒϒ'C – ϒα = B Where ϒ=(ϒ1,ϒ2,...ϒn)’ is a column vector and ϒ’ its transpose C=(c1,c2,…,cn)’ and B=(b1,b2,…bn)’ are a columns vector And...
  17. bornofflame

    [LinAlg] Describe Ker(T) using set notation for T:P^1 -> R

    Homework Statement 2. Let ##T: \mathbb{P}^1 \rightarrow \mathbb{R} \text{ be given by } T(p(x)) = \int_0^1 p(x)~dx## Describe ##Ker(T)## using set notation. Homework Equations ##p(x) \in \mathbb{P}^1~|~ p(x) = a_0 + a_1x## The Attempt at a Solution ##T: \mathbb{P}^1 \rightarrow \mathbb{R}##...
  18. T

    I Axiom of Choice: Disjoint Family ##\Rightarrow ## Power Set

    So apparently the proof involves a trick that converts the problem of a general power set ##\mathscr{P}(M)## of some set ##M## which has of course the property of not having pairwise disjoint set-elements to a problem that involves disjoint set-elements. I do not understand why this trick is...
  19. R

    Write out the following set by listing their elements....

    Homework Statement Write out the following set by listing its elements between braces: {X : X ⊆ {3,2,a} and |X| = 4} Homework EquationsThe Attempt at a Solution My book tells me that it is ∅, but couldn't X have repeated elements? so X = {3,2,a,3}, {3,2,a,2} etc for example??
  20. Math Amateur

    MHB Modules Generated by Sets of Submodules .... .... Bland Problem 2, Problem Set 4.1 .... ....

    I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.1 Generating and Cogenerating Classes ... ... I need some help in order to make a meaningful start on Problem 2, Problem Set 4.1 ... Problem 2, Problem Set 4.1 reads as follows:( *** NOTE ...
  21. Math Amateur

    MHB Direct Sums and Factor Modules .... Bland Problem 14, Problem Set 2.1

    I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need help to make a meaningful start on Problem 14 of Problem Set 2.1 ... Problem 14 of Problem Set 2.1 reads as follows:I am somewhat overwhelmed by...
  22. R

    Sketch the following set of points in the xy plane

    Homework Statement {(x,y) ∈ ℝ^2 : (y-x)(y+x) = 0 } Homework EquationsThe Attempt at a Solution [/B] Is the reason the answer is the union of y = -x and y = x because if you divide (y-x)(y+x) = 0 by y-x you get y = -x and if you divide (y-x)(y+x) = 0 by y+x you get y = x? and if you...
  23. N

    Valve to vent entire volume upon reaching a set pressure

    Greetings, I have an experiment that pressurizes a small volume at variable rates. 1, 2, and 3 psi/sec. I am trying to think of a way to reproducibly drop the pressure of the container by a known amount while it is being pressurized. Are there valves for this type of experiment? What are...
  24. Mr Davis 97

    Showing that the empty set is subset of every set

    Homework Statement Let ##J = \emptyset## and ##A## be any set. Then ##J \subseteq A##. Homework EquationsThe Attempt at a Solution Proof: Suppose that it is false that ##J \subseteq A##. Then ##\exists x (x \in J ~~\text{and}~~ x \not \in A)## is true. But this is a contradiction, since...
  25. Math Amateur

    MHB Start on Bland Problem 1, Problem Set 4.1: Generating & Cogenerating Modules

    I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.2 Noetherian and Artinian Modules ... ... I need some help in order to make a meaningful start on Problem 1, Problem Set 4.1 ... Problem 1, Problem Set 4.1 reads as follows: Can someone...
  26. S

    MHB Prove: 2ε{a,2,b} in Set Theory

    Prove in any axiomatic set theory that:2ε{a,2,b} , where a,b are letters
  27. bornofflame

    [LinAlg] Set Notation, Subspaces, Bases, Ranges, & Kernels

    Homework Statement I don't want to clog up the forums with a few "small" problems so I am lumping them together here. 2. Let ##T:P^1 → R \text { be given by } T(p(x)) = \int^b_a p(x)dx##. Describe Ker(T) using set notation. 3. Let ##H = \left\{f ∈ C[a, b] | f'(x) ≥ 0 ~\text for...
  28. Math Amateur

    MHB Finitely Generated Modules - Bland Problem 1(a), Problem Set 2.2

    I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.2 Free Modules ... ... I need someone to check my solution to the first part of Problem 1(a) of Problem Set 2.2 ... Problem 1(a) of Problem Set 2.2 reads as follows: My solution/proof of the...
  29. Math Amateur

    Finitely Generated Modules - Bland Problem 1(a), Set 2.2

    Homework Statement I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.2 Free Modules ... ... I need someone to check my solution to the first part of Problem 1(a) of Problem Set 2.2 ... Problem 1(a) of Problem Set 2.2 reads as follows: Can...
  30. T

    MHB Classicists' Favorite Epic Poets: Survey Results

    A number of classicists were asked to identify their favorite epic poets. The results are summarized below. 62 appreciate Homer, 40 appreciate Virgil, 5 appreciate Gomer, 2 appreciate Homer and Virgil and Gomer, 3 appreciate Virgil and Gomer, 20 appreciate Homer and Virgil, 42 appreciate Homer...
  31. Math Amateur

    MHB Ring Direct Products .... Bland Problem 3(a), Problem Set 2.1, Page 49 ....

    I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need someone to check my solution to Problem 3(a) of Problem Set 2.1 ... Problem 3(a) of Problem Set 2.1 reads as...
  32. Math Amateur

    Ring Direct Products .... Bland Problem 3(a), Problem Set 2.1

    Homework Statement I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need someone to check my solution to Problem 3(a) of Problem Set 2.1 ... Problem 3(a) of Problem Set 2.1 reads as follows: Homework...
  33. Math Amateur

    MHB Checking My Solution to Problem 2(c) of Problem Set 2.1: Seeking Critique

    I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need someone to check my solution to Problem 2(c) of Problem Set 2.1 ... Problem 2(c) of Problem Set 2.1 reads as follows:My attempt at a solution...
  34. Math Amateur

    Direct Products .... Bland Probem 2(b), Problem Set 2.1 ....

    Homework Statement I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need someone to check my solution to Problem 2(b) of Problem Set 2.1 ... Problem 2(b) of Problem Set 2.1 reads as follows: Homework...
  35. P

    MHB How can i set this problem as a continuous markov chain?

    I request your help in order to know, how can i configure this problem as a continuous markov chain, need to define the main variable, the states, transition rates, and the matrix. I thought that it could be relationed with the independent status of the machines, because if the machine 1 is...
  36. R

    I Why does bent space set objects in motion?

    Two stationary masses will attract each other. That is, they start moving towards each other. For example, a stationary apple will fall to earth. I can see bent space affecting the trajectory of a moving object. ...but how does bent space explain that stationary objects start moving?
  37. Z

    Is the Notation Implied for a Singleton Set or Can It Have Multiple Elements?

    Homework Statement For the following notation, D \subseteq \{ z | \exists x,y \in S (z = x - y ) \} I'm wondering if S can only have one element, or does the notation imply that | S | > 1 Homework EquationsThe Attempt at a Solution For example, if I have S = \{ 3 \} is z = 3 - 3? Or...
  38. Dyatlov

    Studying Which QFT Lecture Series Includes Unitary IR of Poincare Group?

    Hello. I self-studied and have a good grasp on QM, statistical mechanics and Group theory. Next step is QFT. There are several sets of video lectures on Youtube about this subject and I am asking for a recommendation (I would like a set of videos which involves the unitary IR of the Poincare...
  39. A

    How to set up download from my website?

    Hi, I have a website and I would like to give viewers an option for downloading a (Mathematica) file. Actually I have a blog in blogger.com which has a menu item to access an index.html file on another hosted website. I would like to store the file on the hosted website and have a button or...
  40. R

    Set Notation Question: Converting to Set Builder Notation | Homework Help

    Homework Statement So I have the set {...(1/8),(1/4),(1/2),(1),(2),(4),(8)...} I am suppose to put it in set builder notation.. Homework EquationsThe Attempt at a Solution my answer was { x = {\frac {1}{2^n} : n \in ℤ } } but my books was { x = {{2^n} : n \in ℤ } } I understand both...
  41. T

    MHB Finding the Set of Ordered Triples of a Ternary Relation on A

    Given that A = {1, 2, 3 ……..20} and R is a ternary relation on A defined by equation x2 + 4y = z .Find the set of ordered triples of R.
  42. olgerm

    I Map possible values of a set with a condition to the naturals

    I want a way to map natural numbers to possible values of set A. It would also be helpful if you could tell me how many possible values are for set A(it depends of k). All that is known about set A is: Non of set A elements is subset to another element of A, but all elements of set A are proper...
  43. ertagon2

    MHB Set Theory Questions (check if right)

    Could someone please check if these are right?
  44. L

    B Find the missing energy value given a set of data (Hypothetical question)

    Hypothetical question: Let's say there's a granite cube with a volume of 60 cubic centimeters. A cannon ball is shot at it, reducing it to rubble, and the kinetic energy of the ball was 10,000 joules. We use the same ball with the same kinetic energy output on a stronger unknown substance with...
  45. soothsayer

    Force between parallel plates of set voltage

    Hi PF, I have a setup with two plates that are connected to two different voltages and separated by vacuum. In my case, one plate is set at -10kV, and the other plate is set at -7.5kV. I know the area of these plates, the separation of the plates (which is much smaller than the plate area), and...
  46. Baris Kalfa

    Demonstrating set properties of a map

    Hello, could you please help me regarding this question about a certain map (application). Homework Statement Demonstrate if A1 ⊂ A2 →ƒ(A1) ⊂ ƒ(A2) 2. Homework Equations ƒ:A→B is a map A1, A2⊂ A The Attempt at a Solution first assumed that (A1∪A2)⊆A ⇒ (ƒ(A1) ∪ ƒ(A2))⊆ ƒ(A) then if A1 ⊂ A2 ∴...
  47. M

    Show that a set of vectors spans a subspace

    Homework Statement Show that {(1, 2, 3), (3, 4, 5), (4, 5, 6)} does not span R3. Show that it spans the subspace of R3 consisting of all vectors lying in the plane with the equation x - 2y + z = 0. Homework EquationsThe Attempt at a Solution I made a matrix of: A = [ 1 3 4 ; 2 4 5; 3 5 6] and...
  48. H

    I Dense set equivalent definitions

    Hello all, I am an undergraduate student who is studying real analysis from Rudin's POMA and I am trying to prove that these two definitions that I have for dense sets are equivalent: 1) Given a metric space X and E ⊂ X ; E is dense in X iff every point of X is a limit point of E or E = X or...
  49. P

    When is an Electric Field eqn set as - or + ?

    Homework Statement Two point charges are placed on the x axis.(Figure 1)The first charge, q1 = 8.00 nC , is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.00 nC , is placed a distance 9.00 m from the origin along the negative x axis. Find the...
  50. Math Amateur

    LaTeX Latex Code for One Set Minus Another .... .... A\B .... ....

    Recently I posted the following text on the Analysis forum ..." ... ... In order to demonstrate that K is closed, we prove that \mathbb{R}^n\K is open. Indeed, choose y \notin K and define O_j = \{ x \in \mathbb{R}^n \ \mid \ \mid \mid x - y \mid \mid \gt \frac{1}{j} \} for j \in \mathbb{N}...
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