Proof Definition and 999 Threads

Homework Statement Let A and B be elements of the line EF such that A=/B prove that the line AB=EFHomework Equations Axiom that two points determine a unique line and that the intersection of two lines has two distinct points then these lines are the same. The Attempt at a Solution [/B] If A...

Homework Statement Hi, As part of the proof that : the set of periods ##\Omega_f ## of periods of a meromorphic ##f: U \to \hat{C} ##, ##U## an open set and ##\hat{C}=C \cup \infty ##, ##C## the complex plane, form a discrete set of ##C## when ##f## is a non-constant a step taken in the...

Homework Statement Homework EquationsThe Attempt at a Solution Hi How do I go about showing ##0 \leq \frac{2x}{\pi} \leq sin x ##? for ## 0 \leq x \leq \pi /2 ## I am completely stuck where to start. Many thanks. (I see it is a step in the proof of Jordan's lemma, but I'm not interested in...

is this a practical way of proving math theorems? i asked because when i tried, it seemed difficult for me to decide as to how exactly i should translate theorems and given statements into logical forms and since there are so many different ways, i do not know which one is correct. For example...

(From Hoffman and Kunze, Linear Algebra: Chapter 6.7, Exercise 11.) Note that ##V_j^0## means the annihilator of the space ##V_j##. V* means the dual space of V. 1. Homework Statement Let V be a vector space, Let ##W_1 , \cdots , W_k## be subspaces of V, and let $$V_j = W_1 + \cdots + W_{j-1}...

When I hear that mass of a particle has managed to hop through a solid barrier ..it tells me that the mass was a variable and not physical at the time.

Is this proof even correct?! It places assumption on a and c NOT BEING ZERO. Thanks in advance. I am new to proofs.

Hello! (Wave) We say that the space $\Omega$ satisfies the exterior sphere condition at the point $x_0 \in \partial{\Omega}$ if there is a $y \notin \overline{\Omega}$ and a number $R>0$ such that $\overline{\Omega} \cap \overline{B_y(R)}=\{ x_0 \}$. Let the function $\phi \in...

Homework Statement Show that if ##G = \langle x \rangle## is a cyclic group of order ##n \ge 1##, then a subgroup ##H## is maximal; if and only if ##H = \langle x^p \rangle## for some prime ##p## dividing ##n## Homework Equations A subgroup ##H## is called maximal if ##H \neq G## and the only...

Homework Statement Let ##f:X \to Y##. Show that ##f## not uniform continuous on ##X## ##\Longleftrightarrow## ##\exists \epsilon > 0## and sequences ##(p_n), (q_n)## in ##X## so that ##d_X(p_n,q_n)\to 0 ## while ##d_Y(f(p_n),f(q_n))\ge \epsilon##. Homework Equations Let ##f:X\to Y##. We say...

Homework Statement Let ##E## be a metric subspace to ##M##. Show that ##E## is closed in ##M## if ##E## is complete. Show the converse if ##M## is complete. Homework Equations A set ##E## is closed if every limit point is part of ##E##. We denote the set of all limit points ##E'##. A point...

Homework Statement Let ##E \subseteq M##, where ##M## is a metric space. Show that ##p\in \overline E = E\cup E' \Longleftrightarrow## there exists a sequence ##(p_n)## in ##E## that converges to ##p##. ##E'## is the set of limit points to ##E## and hence ##\overline E## is the closure of...

Homework Statement Prove that if a² + ab + b² = 0 then a = 0 and b = 0 Hint: Recall the factorization of a³-b³. (Another solution will be discussed later when speaking about quadratic equations.) Homework Equations a² + ab + b² is close to a² + 2ab + b² = (a+b)² a³-b³=(a-b)(a²+ab+b²) The...

Prove (formall y) in predicate calculus : $\neg\exists y\,\forall x\,(x\in y\leftrightarrow \neg x\in x)$.

Homework Statement I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...). Can someone please help me out where I've gone wrong: struggling to spot it...

Homework Statement let fx, gx be continuous in [a,b] and differentiable in (a,b). at the end of the interval f(a) >= g(a). and f'(x) >g'(x) for a<x<b. proof f(x) > g(x) for a<x<=b Attempt: There is a statement says that if the f'x = g'x for x in [a,b] , then there exists k such that f'x -...

Homework Statement p(x) = 0.2*(x-1)^5, q(x) = 4x-6 The Attempt at a Solution I took the diffrence h(x) = p(x) - q(x) h'(x) = ((x-1)^4) - 4 got two solutions for h'(x)=0.

Homework Statement I understand the proof of the implicit function theorem up to the point in which I have included a photo. This portion serves to prove the familiar equation for the implicit solution f(x,y) of F(x,y,z)=c. My confusion arises between equations 8.1-4 and 8.1-5 when it is stated...

Found an article online detailing a proof of the Riemann Hypothesis: << link deleted by mentor - unacceptable source >>

For some values Q and n being integers, prove that n(n^4 - 1) = 10Q. So I've tried this with induction, but it gets pretty messy pretty quickly. So I can see that the LHS will be even no matter what, but I'm not sure where to go beyond this.

Homework Statement Prove: If p is prime and m, n are positive integers such that p divides mn, then either p divides n or p divides m. Is anyone willing to look through this proof and give me comments on the following: a) my reasoning within the strategy I chose (validity, any constraints or...

There is a graph showing n on its x-axis and its total stopping time on its y axis. From here we can see that the points on the graph are not random at all; they have some kind of geometric pattern that is due to the 3x+1 in the odd case and x/2 in the even case. I have seen many attempts to...

Homework Statement http://prntscr.com/dcfe0u Homework EquationsThe Attempt at a Solution So I'm not really strong in proofs but I think you may be able to do something like this:$$lnL = \frac{ln(1+1/x)}{x}$$ $$lnL = \frac{1/x^2}{1+1/x}$$ and then more simplifying I get something like: $$lnL =...

Mentor note: moved to the homework section Claim: all numbers divisible by 4 are divisible by 2. Premise: let p(n) return 4n, I.e., the function covers all numbers divisible by four. Reasoning: Let n equal 1 in the base case P(n) is divisible by 2 P(n+1) is divisible by 2 By induction all...

I am using Lang's book on complex analysis, i am trying to reprove theorem 4.1 which is a simple theorem: Let Compact(S \in \mathbb{C}) \iff Closed(S) \land Bounded(S) I will show my attempt on one direction of the proof only, before even trying the other direction. Assume S is compact Idea...

Proof: If either x or y is zero, then the inequality |x · y| ≤ | x | | y | is trivially correct because both sides are zero. If neither x nor y is zero, then by x · y = | x | | y | cos θ, |x · y|=| x | | y | cos θ | ≤ | x | | y | since -1 ≤ cos θ ≤ 1 How valid is this a proof of the...

The thread I wanted to post my question on got closed. Recapitulating: The best (simplest) account I have found to date for the Bell inequality (SPOT stands for Single Photon Orientation Tester): Imagine that each random sequence that comes out of the SPOT detectors is a coded message. When...

Salutations, friends from afar. The question I have is mundane, but I felt I should be sure. It is basically to spot the insufficiency in this proof for Zorn's Lemma: If every chain in a partially ordered set M has an upper bound, then M contains a maximal element. Proof: 1. For a set X, take...

What is the proof of the fact that for an isolated system, entropy can never decrease?

Homework Statement How can I show that if a vector (in a vector space V) cannot be written as a linear combination of a linearly independent set of vectors (also in space V) then that vector is linearly independent to the set? Homework Equations To really prove this rigorously it would make...

Homework Statement Let ##x\in \mathbb{R} ## Prove the conditional statement that, if ## x>-1## then ## x^2 + \frac {1}{x^2+1} \geq 1## 2. The attempt at a solution Suppose ## x>-1## is true. Then ## x^2>1## Then ## \frac{1}{2}>\frac {1}{x^2+1}## Then ##x^2+ \frac{1}{2}>x^2+\frac...

I'm still learning English, had to use dictionary and translator, so I'm sorry if its unclear, i will try to explain it more if needed. Homework Statement For n belonging to N when n is even and n > 3, prove that (4^(n-3) + 5^(n-3) + 9) is divisible by 9 Homework Equations 3. The Attempt at...

hi guys, I'm supposed to write a paper and do some research on all aspects of drilling regarding torque and force need to drill an oil well and everything from start to finish and to provide mathematical proof and calculations. I don't know where to start and what are the equations used to...

Given :- $$g(f(x_1)) = g(f(x_2)) \implies x_1 = x_2$$ Question :- Check whether ##g(x)## is injective or not. Now this is of-course false; counter examples are easy to provide. But I proved that ##g(x)## must be one-one even after knowing the fact it must not. Here is the proof :- Let...

We have, e^(ix)=cosx+isinx So, e^(i*i)=cosi+isini Or e^-1=cosi+isini Or 1/e + 0*i= cosi+isini So, cosi=1/e and sini=0 But that's not the value of sin(i) that I found on the internet. These values are not even satisfying cos^2(x)+sin^2(x)=1. What did I miss?

Hello Anyone, Could you help me in finding the torque req. for a cap to leak proof? My cap (polyproplene) which dia. was 32mm and its detail specs are, thread major dia.- 28.5mm, min. dia. - 26mm, pitch - 3mm, thread angle-45deg which has a EPDM rubber seal placed inside (outer dia 26.5mm &...

Homework Statement Prove that, given a metric ##g_{ij}## such that ##ds^{2}=g_{ij}dx^{i}dx^{j}##, where ##x^{r} = x^{r}(\lambda)## , we have the following result for the arc length: $$ L(p,q) = \int_{p}^{q} ds = \sqrt{ g_{ij} \frac{dx^{i}}{d \lambda} \frac{ dx^{j}}{d \lambda} } d \lambda $$...

How do I begin proving: sum(k>=1)8/(k^4+4)=pi*coth(pi)-1? I got this from Mathematica. Thanks in advance for any help.

Homework Statement Provide a complete formal proof that ## \vdash ((A \rightarrow B) \rightarrow C) \rightarrow (B \rightarrow C)##. Homework Equations I am only allowed to use modus ponens and these four 'sentential logic' axioms: A1 ## \neg \alpha \rightarrow (\alpha \rightarrow \beta)## A2...

I can't find a derivation of d'Alembert principle. Wikipédia says there is no general proof of it. Same with stackexchange. I find it surprising so I thought I'd come here to check with you guys. D'Alembert principle has indeed no proof ?

Homework Statement Prove the following statement: ln|1+\sigma x | = \frac{1}{2} ln|1-x^2| + \frac{\sigma}{2} ln| \frac{ |1+x|}{|1-x|} Homework EquationsThe Attempt at a Solution Starting from right to left would be easier: = \frac{1}{2} ln|(1+x)(1-x)| + \frac{\sigma}{2} ln| 1+x| -...

Homework Statement Proof that the limit of the function below doesn't exists. limx-->1 1/(x-1)Homework EquationsThe Attempt at a Solution Lets assume that limit L exists. So if (1) 0< |x-1| < δ then (2) |1/(x-1) - L| < ε at the book they gave an example by giving a value...

If $X$ is a set, then the power set $P(X)$ of a set is the set of all subsets of $X$. I need to decide whether the following statements are true or false and prove it: (i) If $Z = X \cup Y$ , then $P(Z) = P(X) \cup P(Y)$. (ii) If $Z = X \cap Y$ , then $P(Z) = P(X) \cap P(Y)$. By examples I...

ABCD is a parallelogram . X is the midpoint of AD & Y is the midpoint of BC. Show that the area of $\triangle {ABX}$ is $\frac{1}{4}$ the area of ABCD Can you help me with this proof ? were should i start ? I think It should be by proving $\triangle{DBC} \cong \triangle{DBA} $ using SAS as...

Homework Statement Hi everybody! I'm struggling to solve the following problem: Let ##< \cdot, \cdot >## be an inner product on the vector space ##X##, and ##|| \cdot ||## is the norm generated by the inner product. Prove that the function ##x \in X \mapsto ||x||^2 \in \mathbb{R}## is...

Homework Statement Can anyone please help me solve these questions? (1) Prove that (A-B) - (B-C) = A-B (2)Simplify (A-( A N B)) N (B-(ANB)) (3) Simplify ( ( A N ( B U C)) N ( A-B)) N ( B U C') (4)Use element property and algebraic argument to derive the property (A-B) U (B-C) = (A U B) - (B N...

this question is a repost from math stackexchange because that guy worded the question so perfectly the question i really wanted to ask about cross products. *please see image below* as far i can understand, the formula for the cross product is basically that the idea of a cross product is sort...

Homework Statement Prove by induction $$w_k = w_{k−2} + k$$, for all integers $$k \ge 3, w_1 = 1,w_2 = 2$$ has an explicit formula $$ w_n =\begin{cases} \frac{(n+1)^2}{4}, & \text{if $n$ is odd} \\ \frac n2(\frac n2 + 1), & \text{if $n$ is even} \end{cases}$$ Homework Equations The Attempt...

is there a proof that the number of even/odd permutation matrices of any nxn, where n is greater than 3, is n!/2? basically, i want to understand the derivation of n!/2. thank you!

Cantor "proved" that if there was a list that purported to include all irrational numbers, then he could find an irrational number that was not on the list. Please consider two scenarios: 1. The list claims to contain all irrationals but doesn't. 2. The list absolutely contains all...