Existence Definition and 570 Threads

Homework Statement I can do the question, but in a different way to the worked solution which I don't understand. So my question is can anyone explain the worked solution which is in point 3 below. The question was to show there is exactly one zero to the function f(x) = Ax^3 - Ax + 1, with...

that a thread about why the world does not exist does not exist?

Is there a mathematical proof for the existence of black hole.

Suppose ##f(x)## is continuous at ##x=c##. Does this imply that ##f(x)## exists in an open neighbourhood of ##c##? I believe it does. If ##f(x)## is continuous then ##\lim_{x\to c}f(x)## exists. But if ##f(x)## is undefined for some values of ##x## in the ##\delta##-neighbourhood of ##c##, then...

So, I am not an expert in quantum physic, I just watched a lot of videos about it. If I understand correctly, particles do not have a particular position as long as you don't observe them. With a certain equation, we can draw a cloud of probabilities which describes how likely the particle is...

Hey, guys! So, I've been wondering. Space and time are not only interrelated, time is the movement of space. So, time is space, yet space is not time. Now, my question. If light exists outside of time, and space is always moving, thus creating time, how does it exist - and how do we experience...

I have read in several articles about quantum physics and consciousness the idea that reality is "flashing in and out of existence". I have copied a quote below from Brandon West about this. Does anyone have more information about any research or theoretical basis of this? Quote: "And...

Or is it only theoretical.

Hello! (Wave) How can we show that there are constants $c_m$ such that: $$\sum_{|a| \leq m} |\xi^a|^2 \leq (1+ |\xi|^2)^m \leq c_m \sum_{|a| \leq m} |\xi^a|^2$$ Could you give me a hint what we could do?

I'm looking into a science fair project involving proving the existence of tritium in the exhaust of a Farnsworth fusor, and was wondering what the ideal method to prove it is. I've thought of three so far. The first is ionizing the gas and analyzing the spectra. The second is placing an alpha...

According Zimmermann in 1953 "evolution is the transformation of the form and mode of existence" so I want want understand what is mode of existence ?

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.1 Introduction to Tensor Products ... ... I need help with another aspect of the proof of Theorem 10.1 regarding the existence of a tensor product ... ...The relevant part of...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.1 Introduction to Tensor Products ... ... I need help with another aspect of the proof of Theorem 10.1 regarding the existence of a tensor product ... ... The relevant part of...

Given three parameters: $$a= \frac{(k-3)^2 \sqrt{v}}{s}, \ \ b = \frac{v}{s}(w-10s), \ \ c = s \sqrt{v}.$$ which exact values I know (that is, I know $v,s,k$ and $w$ exactly). I need to guarantee that $a<0$ (this is always satisfied in my calculations!) and $$0<b<1.08148a^2$$ For instance, if...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.1 Introduction to Tensor Products ... ... I need help with the proof of Theorem 10.1 on the existence of a tensor product ... ...Theorem 10.1 reads as follows: In the above text...

I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ... I am focused on Section 10.1 Introduction to Tensor Products ... ... I need help with the proof of Theorem 10.1 on the existence of a tensor product ... ... Theorem 10.1 reads as follows:In the above...

Homework Statement For what value of the constants a and b such that the following limit exists? lim {(ax+|x+1|)|x+b-2|}/|x+1| x->-1 help me ,thx Homework EquationsThe Attempt at a Solution first, I know that I should cancel the absolute value at denominator of x+1. but i don't how to...

Hi. I think there has been research about the idea that time may not exist on the very fundamental level of reality. Does anyone know if space exists at that same level? I have read somewhere that at the Planck level, which is the smallest level physicists have gone to, time and distance drop...

Homework Statement Prove that for all n ≥ 1, there exists a polynomial f(x) ∈ ℚ[x] with deg(f(x)) = n such that f(x) is irreducible in ℚ[x]. Homework Equations In mathematics, a rational number is any number that can be expressed as the quotient or fractionp/q of two integers, a numeratorp...

what value of the constants a and b if the following limit exists lim (ax + |x + 1|)|x + b − 2| |x + 1| x→−1 |x|= x for x≥ 0 and |x|= -x for x<0 |x+1|= x+1 for x≥ -1 and |x+1|= -(x+1) for x<-1 I don't know how to determine |x + b − 2| is positive or negative. i know that if limit...

Homework Statement Express the following using existential and universal quantifiers restricted to the sets of Real numbers and natural numbers Homework EquationsThe Attempt at a Solution I believe the existence of rational numbers can be stated as: ##(\forall n \in \Re)(\exists p,q \in...

If $G$ is a finite group, show that there exists a positive integer $N$ such that $a^N = e$ for all $a \in G$. All I understand is that G being finite means $G = \left\{g_1, g_2, g_3, \cdots, g_n\right\}$ for some positive integer $n.$

Hello! (Wave) We have the space $x^2+y^2 \leq 4$ and we consider the Cauchy problem $y'=\cos x-1-y^2, y(0)=1$. I want to find for which $b>0$ the Picard theorem ensures the existence of the solution on $(-b,b)$. I have thought the following: Since $g(x,y):=\cos x-1-y^2$ is continuous as for...

Prove that there exists a triangle which can be cut into 205 congruent triangles.

Hi, layman here, I have often read that because of time dilation, we would never see any infalling matter actually crossing the event horizon, it would just look more and more redshifted towards becoming invisible, even for infrared or microwave / radio detectors, but never becoming part of the...

Hello, Since it was mentioned in my textbook, I've been trying to find Riemann's proof of the existence of definite integrals (that is, the proof of the theorem stating that all continuous functions are integrable). If anyone knows where to find it or could point me in the right direction, I...

This is not a serious post; I was wondering why there must be so much speculation over extraterrestrials exist or not, while they had proposed with the quantum theory on the "existence of the scrutinized" so everything MUST be seen at all times, which is only possible if life exists alongside...

Hey! :o I want to check if we can always find a solution of a linear differential equation of first order in the polynomial ring $F[z]$. I have done the following: The general linear differential equation of first order is $$ax'(z)+bx(z)=y(z)$$ where $x,y \in F[z]$. Or is it possible that...

Hello, I have a question about the interaction between particles. Maybe it's a simple question, but it's bothering me. Consider Coulomb's law. From Wikipedia we have a simple definition to illustrate: "The magnitude of the electrostatic force of interaction between two point charges is directly...

Homework Statement Given the equation dy/dx = y^4 - x^4, y(0) = 7, determine whether the existence/uniqueness theorem implies that the given initial value problem has a unique solution. Homework Equations Existence/Uniqueness Theorem The Attempt at a Solution To my understanding, you must...

Hello, In my book on Differential Equations, There is a Theorem that states: "Consider the IVP $\d{y}{x}=f(x,y), y(x_0)=y_0$ If $f(x,y)$ and $\pd{f}{y}$ are continuous in some $a<x<b$, $c<y<d$ containing the point $(x_0,y_0)$, then the IVP has a unique solution $y=\phi(x)$ in some Interval...

I'm struggling to get started with the proof that an open interval D containing x0 exists such that f'(x) ≠ 0 for all x∈D, given f'(x0)≠0. It seems like it should be easy but I've been scratching around for an hour now and have gotten nowhere, could anyone give me some advice to help me along?

Hello, Cosmology for the layman says that there was a time t=0 when the universe was created out of infinitesimal length distance and before that nothing existed not even time. OK, but this rests on the assumption that there is always a manifold from which we cut off our space slices in the...

"Apparently, they have spotted a ‘woman like’ creature on Mars with the help of their Curiosity Rover".My question is: At low temperature & cosmic radiation, along with low gravity can we find a living organism? Is the above quoted lines was true? i have noted this news recently on facebook...

What I understood so far is that whole universe was born from a single point at which there was no time (or all the time was at single point - no present, no future) and then a big bang happened (may be), creating time, energy, mass etc. I want to learn physics at much deeper levels. So, I...

How do I derive an expression or algorithm that determines the existence of a point or set of points within k distance of an N number of other fixed, given points? In application, I expect to only need to determine that this region exists for three to five points. This is part of a greater...

I have a doubts related to gravity How do this gravity come into existence? What is a cause of gravity? Why two masses are attracted due to gravity?

I do not know if uranium monoxide exists or not because I can't find anything about it on the internet, but i can make a lewis dot structure of it. Can somebody help about this?

I am reading an article[1] that states: Let k be a fixed local field. Then there is an integer q=pr, where p is a fixed prime element of k and r is a positive integer, and a norm |.| on k such that for all x∈k we have |x|≥0 and for each x∈k\{0} we get |x|=qm for some integer m. This norm is...

It seems to me that, although QM involves many mathematical constructs that are a bit daunting and may take a long time to master, this is not necessarily an insuperable barrier to the learner's progress. What is perhaps more potentially confusing is, identifying all the subtle ways that...

2nd order ODE has a form y''+p(x)y'+q(x)y=f(x)and if we assume f(x)=/=0 for every x, then y''+p(x)y'+q(x)y=/=0 so in this case we can't specify general solution of 2nd order ode?

I'm a student trying to understand the nature of things. My existence seems rather implausible to me but as best I can tell I am here and delighted to be. I look forward to being a member of this community. Thank you for the opportunity.

I have a question about photon speed and time releation. When photon is speeding at the speed of light, the time for him stops as i understand. So that means that from photon perspective to travel 1 light year takes no time and that means, that from it's perspective at the same time it is in all...

Im trying to get some intuition for convex neighbourhoods which is neighbourhoods ##U## such that for any two points ##p## and ##q## in U there exists a unique geodesic connecting ##p## and ##q## staying within ##U##. QUESTION 1: These kind of neighbourhoods can be shown to always exist for...

Hello friends! I am a newbie here. I love quantum physics very much... especially the standard model of fundamental particles, QED, QCD, etc. I have an urge to create my own theory on space quanta (that's for another time...) but my main question is: Does anti-particle of a photon exist (i.e...

Given \frac{dy}{dx} =2xy^2 and the point y(x_0)=y_0 what does the existence and uniqueness theorem (the basic one) say about the solutions? 1) 2xy^2 is continuous everywhere. Therefore a solution exists everywhere 2) \frac{\partial }{\partial y} (2xy^2) = 4xy which is continuous everywhere...

As i read when the big Bang happened,it was in a hot dense state for the first million years. Then the gases started to collect together and cool down,to form stars. (Sorry if i`m being wrong). So when did and how did the first ray of visible light came into existence?

Hi, let E be a measurable subset of the Real line with m(E)>1 . I want to show there are x,y in E so that x-y is in ## \mathbb Z-{0} ##. My idea is to restrict the quotient ## \mathbb R / \mathbb Z |_E ##. This quotient cannot be contained in [0,1], since m([0,1])=1 and m(E)>1. From this I want...

from what i understand they pop into and out of existence because + 1 - 1 = 0 and because quantum mechanics... and that's the same reason we have matter in the first place, right? because we had anti matter and matter (from virtual particles, right?) in the beginning of the observable...

Hello! (Wave) I want to describe an algorithm that given an unsorted array $B$ that stores $m$ integers, and any integer number $y$, determines if there are two elements of the array of which the quotient is equal to $y$. The time complexity of the algorithm should be $O(m \log m)$. We have to...