# 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. ### I Bloch Analysis proof of Theorem 2.5.5 (Definition by recursion)

Want to understand how set C contains ##N## x H. H is only defined to be a set with element e and as the domain/range of function k. Is this enough information to conclude that the second set in the cartesian product W is H and not a subset of H? My thinking is to show that ##N## and H satisfy...
2. ### I Number of Binary Operations on a Set with a Special Property

Hello all, The question I am tackling is as follows: I was wondering if any of you could look over my solution and tell me if my logic is correct. Any feedback would be great!
3. ### Exploring the Non-Existence of a Maximum in the Set (0,2)

For this, I am trying to understand why the set ##(0,2)## has no maximum. Is it because if we say for example claim that ##a_0 = 1.9999999999## is the max of the set, then we could come along and say that ##a_0 = 1.9999999999999999999999999999## is the max, can we continue doing that a...
4. ### I Definition of a "zero mapping"

In the context of the mappings of a set S into itself, when S is not number system with a zero, what is the customary definition for "zero mapping"? ( ChatGPT says that its a mapping that maps each element of S to some single element of S , i.e. maps all elements to some constant. )
5. ### B Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold?

I am thinking why the following holds: Let f be a smooth function with f: Ω⊂R^m→R. Why is the set {(x,y)∈Ω×R|y=f(x)} a manifold? Would be helpful if you are providing me some guidance or tips:)
6. ### Describe the set of points that satisfy ##(x-4)(z-2)=0##

We are told that ##(x-4)(z-2)=0## The ##0## refers to what variable? The ##z=2## i think the sketch on diagram may be misleading (not to scale). Why have the ##x## crossing the axis on negative side and same applies to ##z##... To put this into context, we may have ##(x,y,z)=(4,y,z)## where...
7. ### I How to determine if a set is a semiring or a ring?

Let E be a finite nonempty set and let ## \Omega := E^{\mathbb{N}}##be the set of all E-valued sequences ##\omega = (\omega_n)_{n\in \mathbb{N}}F##or any ## \omega_1, \dots,\omega_n \in E ## Let ##[\omega_1, \dots,\omega_n]= \{\omega^, \in \Omega : \omega^,_i = \omega_i \forall i =1,\dots,n...
8. ### Python FineTune the Pixel2Style2Pixel model with my custom data set

I want to fine-tune the Pixel2Style2Pixel model with my custom data set, but I keep getting an error when I'm trying to load in the pre-train weights. Here is my code : # Load the pre-trained model os.chdir("/content/pixel2style2pixel") from models.psp import pSp config = { "lr": 0.0001...

15. ### Need Aid On This Problem Set (Combinations of Month Numbers in 10 Years)

TL;DR Summary: Eight Exact To Get 49 Please advise if I am wording this problem correctly and what are the solution (is there some equation for combinations )/ Answers:SET of numbers 1,2,3,4,5,6,7,8,9,10,11,12 months of the year. Within the exact time frame of 10 years I MUST choose a number...
16. ### How to set up MPAndroid Chart?

Hi everyone Can someone show me how to add MPAndroid Chart to Android Studio Dolphin? I've tried following the instructions given at https://www.geeksforgeeks.org/how-to-create-a-barchart-in-android/ Navigate to the Gradle Scripts > build.gradle(Module:app) and add the below dependency in the...
17. ### I May I use set theory to define the number of solutions of polynomials?

Let ##Q_{n}(x)## be the inverse of an nth-degree polynomial. Precisely, $$Q_{n}(x)=\displaystyle\frac{1}{P_{n}(x)}$$, It is of my interest to use the set notation to formally define a number, ##J_{n}## that provides the maximum number of solutions of ##Q_{n}(x)^{-1}=0##. Despite not knowing...
18. ### Two vectors forming right handed set?

I am confused by a question. I thought "right handed set" only applied to sets of three vectors. However I have been given 2 vectors and asked "check whether they are perpendicular to each other and if they form a right handed set. If they don't form a right handed set, the second vector must be...
19. ### Determine the set of odd primes ## p ##?

Let ## p ## be an odd prime. Then ## 23 ## is a quadratic residue modulo ## p ## if ## (23|p)=1 ##. Applying the Quadratic Reciprocity Law produces: ## (23|p)=(p|23) ## if ## p\equiv 1\pmod {4} ## ## (23|p)=-(p|23) ## if ## p\equiv 3\pmod {4} ##. Now we consider two cases. Case #1: Suppose ##...
20. ### I Set up equations for shape

I have a shape based on the idea of having a string, a closed loop, that is sitting outside a rectangle. The string is d longer than the circumference of the rectangle. I noted the sides as a and b. The shapes is formed by drawing a line around the rectangle with the string as a constraint of...
21. ### I Does a set of matrices form a ring? Or what is the algebraic structure?

Square matrices are closed under addition and their own form of multiplication, but in general do not commute. What algebraic structure then describes this, along with polynomials of matrices and allows us to amend with other operations, such as differentiation or integration defined on these...
22. ### A Diffraction from a set of concentric rings with random phase

I have been considering the properties of a Diffractive Optical Element (DOE) consisting of a very large number of concentric rings of equal (small) width, where the thicknessses of the rings are such as to produce random phase shifts in the range 0 to 2pi. I think I understand the behaviour of...
23. ### Determine if the given set is Bounded- Complex Numbers

My interest is only on part (a). Wah! been going round circles to try understand why the radius = ##2##. I know that the given sequence is both bounded and monotonic. I can state that its bounded above by ##1## and bounded below by ##0##. Now when it comes to the radius=##2##, i can also say...
24. ### I Is the solution to this problem as trivial as I think?

The problem goes as follows: Let ##M, N## be sets and ##f : M \rightarrow N##. Further let ##L \subseteq M## and ##P \subseteq N##. Then show that ##L \subseteq f^{-1}(f(L))## and ##f^{-1}(f(P)) \subseteq P##. Obviously, I would simply use the definition of a functions inverse to obtain...
25. ### Set properties of even (##E##) and odd (##I##) integers

Problem Statement : I copy and paste the problem as it appears in the text (Lang, Basic Mathematics, 1971). Attempt : There are several questions in both a) and b) above. I type out the question and my answer each time. a) (i) Show that addition for ##E## and ##I## is associative and...
26. ### Problem set with 5 proofs involving odd, even, parity, etc.

help me in my problem set qs
27. ### Determine (with proof) the set of all prime numbers

Proof: Let ## p ## be the prime divisor of two successive integers ## n^{2}+3 ## and ## (n+1)^{2}+3 ##. Then ## p\mid [(n+1)^{2}+3-(n^{2}+3)]\implies p\mid (2n+1) ##. Observe that ## p\mid (n^{2}+3) ## and ## p\mid (2n+1) ##. Now we see that ## p\mid [(n^{2}+3)-3(2n+1)]\implies p\mid...
28. ### B Destructive Interference in the sound of multiple firecrackers set off at once?

There is a massive and continuous fireball as fire crackers are exploding, generating thousands of shockwaves. Perhaps they are bouncing off each other and cancelling each other out like noise cancelling headphones,
29. M

### I Approximate new acorrelation given previous acorrelation and a new set of data?

Hi PF! The autocorrelation coefficient ##\rho## is defined as $$\rho_k \equiv \frac{\sum_{t=k+1}^T (x_t - \bar x)(x_{t-k} - \bar x)}{\sum_{t=1}^T(x_t-\bar x)^2}$$ Now suppose we calculate ##\rho## through ##T##, but are then given a new data at time ##T + \Delta t##. Is there a way to...
30. ### I How can I use the concept of a proper map to show that a set is bounded?

Dear Everybody, I am having some trouble with proving this set ##S=\{(x,y)\in \mathbb{R}^2: 3x^2-4xy+5y^2 \leq 5\}## is bounded. Find a real number ##R>0## such that ##\sqrt{x^2+y^2}\leq ## for all ##(x,y)\in S.## My attempt: ##3x^2-4xy+5y^2 =3x^2+(x-y)^2-(x+y)^2+5y^2 \\ \leq...
31. ### I Will a spherical mass be set in motion by a spherical shell rotating around it?

In general relativity, rotation of mass gives rise to framedraging effects, just like linear motion does, because of the off-diagonal components in the mass-energy-momentum tensor. So around Bonnor beams there is framedragging, as well around a rotating mass. Now imagine a spherical rotating...
32. ### Difficulty visualizing given set

Okay so I know, that if the radius is 0, the z coordinate will run from -1 to +1. If the radius tends to one, the z coordinate will tend to 0. But I still cannot imagine how this set looks like, help would be appreciated. Thank you.
33. ### Are the states (or set of states) absorbing, transient or recurrent?

Summary: Determine the absorbing states & communication classes of the given matrix. Hello everyone, If we have a state space of S = {1,2,3,4} and the following matrix: \begin{bmatrix} 0 & 1 & 0 & 0\\ 0 & 0 & 1/3 & 2/3\\ 1 & 0 & 0 & 0\\ 0 & 1/2 & 1/2 & 0\\ \end{bmatrix} Now, given the...
34. ### Proving that an Integer lies between x and y using Set Theory

## y-x \gt 1 \implies y \gt 1+x## Consider the set ##S## which is bounded by an integer ##m##, ## S= \{x+n : n\in N and x+n \lt m\}##. Let's say ##Max {S} = x+n_0##, then we have $$x+n_0 \leq m \leq x+(n_0 +1)$$ We have, $$x +n_0 \leq m \leq (x+1) +n_0 \lt y+ n_0$$ Thus, ##x+n_0 \leq m \lt...
35. ### In Python flask I am trying to set up the SMTP for emails in outlook

I am trying setting up flask email for outlook. I had it working with gmail I found this link https://superuser.com/questions/1521236/how-to-allow-less-secure-app-access-in-microsoft-email I tried MAIL_SERVER= 'smtp.office365.com' MAIL_PORT = 587 MAIL_USE_TLS = True...
36. ### Prove that ## aa_{1}, aa_{2}, ...., aa_{n} ## is also a complete set?

Proof: Suppose for the sake of contradiction that ## aa_{i}\equiv aa_{j}\pmod {n} ## for some ## i,j\in\mathbb{Z} ## such that ## 1\leq i<j\leq n ##. Then ## aa_{i}\equiv aa_{j}\pmod {n}\implies n\mid (aa_{i}-aa_{j})\implies n\mid [a(a_{i}-a_{j})] ##. Note that ## n\mid b ## if ## n\mid (ab) ##...
37. ### Determine the set of values of ##n## that satisfy the inequality

Find solution here; Ok i just want clarity for part (a), My approach is as follows, since we want positive integer values that satisfy the problem then, ##\dfrac {n^2-1}{2}≥1## I had earlier thought of ##\dfrac {n^2-1}{2}≥0## but realized that ##0## is an integer yes but its not a positive...
38. ### VFD harmonics effects on generator set

I would like to use VFDs for motor sizes ranging from 0.4kw to 15kw. My idea here is to reduce the generator foot print to the lowest possible value. My thinking is that, theoretically, I could use a 25kva generator set to drive a 20hp motor (80% operating capacity) and since the VFD eliminates...
39. ### Find the set of possible values of ##a## - Modulus Graph

My interest is on question 9. b(i) Find the question and solution here; I understand that ##a## should be less than ##2## because when ##a=2##, the two equations shall have same gradients which implies that the two lines are parrallel to each other. Now to my question, this solution does not...
40. ### MHB Set Problems: Is My Statement about Circles True?

Is the statement that I have circle is true ? Because I feel like the solution in my textbook is wrong, I only learn that empty set is a subset of every set but it is not an element of a set.
41. ### I What is the construction of charts for the tangent bundle on the unit circle?

Hello there! Reading the textbook on differential geometry I didn't get the commentary. In Chapter about vector bundles authors provide the following example Let ##M=S^1## be realized as the unit circle in ##\mathbb{R}^2##. For every ##x\in S^1##, the tangent space ##T_x S^1## can be identified...
42. ### LaTeX Latex Problem for Set B Minus set B' that is B \ B' (SOLVED)

Can someone show me how to include the set minus operation in latex code ... obviously there is a difficulty that the symbol \ within latex delimiters just leaves a space ... ... so B \ B' doesn't result in B \ B' Peter (SOLVED) B \text{ \ } B' works ... ... ... ... ... B \text{ \ } B'
43. ### How to Efficiently Handle Set Operations Without Inbuilt Functions?

ok we shall have ##(A-B)∩(A-C)= [1,y]∩[1,2,x,y]=[1,y]## correct?
44. ### A Understanding Cantor set C in Ternary form with 1/n factor in front C

Dear Everybody, I am confused by ##1/n C##, where C is a cantor set in base 3 and ##n\geq2##. I can understand the construction of the normal Cantor set. How do I comprehend this set with this extra condition. Do I multiply the set with ##1/n## or not? Thanks, Cbarker1 mentor note...
45. ### Is there a way to prove that a set is bounded using calculus techniques?

I know that for a set to be bounded it is bounded above and below, for the bound below is it 0 and n cannot equal 1 and u paper bound is inf but how do I prove that it is bounded?
46. ### Define a Dedekind cut and show the given set is(n't) a Dedekind cut

a) a subset ##L\subset \mathbb{Q}## is a Dedekind cut if ##L## is proper, ##L## has no maximal element, and $$\forall a,b\in \mathbb{Q}, [(a<b)\land( b\in L)\Longrightarrow a\in L]$$ b) Is ##P=\{x^4|x\in L\}## a Dedekind cut? P is proper: (a\in L)\Longrightarrow (a^4\in P)\Longrightarrow...
47. ### One set v is a linear combination of u. Prove u is linearly dependent

Hi Everybody, I am having some difficulties on the prove this problem. I picked a nice example when I was trying to think about the proof. Let ##s=3## and ##t=2##. Then ##u1=c1v1+c2v2, u2=c3v1+c4v2, u3=c5v1+c6v2##. Then a linear combination of u: ##K1u1+K2u2+K3u3=0##. I grouped both linear...
48. ### Cylindrical Permeability Problem: Help on how to set up

I was asked to give an estimate for a three dimensional permeate problem and I need an assist in how to setup a model equation. Picture a 6" underground cylindrical bore. The depth of the cylindrical bore is 150 feet. The bore is sealed at the bottom and the permeability below the bore bottom...
49. ### A Can Einstein Tensor be the Product of Two 4-Vectors?

In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ] Since Einstein equation is G = 8πGT, I am...
50. ### Show that gcd(a,b) is the smallest positive element in the set {ma+nb}

##m##, ##n##, ##a##, and ##b## are in ##\mathbb{Z}##. The set of natural numbers is an abelian group, so ##\{ma+nb|m,n\in\mathbb{Z}\}## is a subset of ##\mathbb{Z}##. ##a ## and ##b## are either relatively prime or not relatively prime. If ##a ## and ##b## are relatively prime, then there are...