Proofs Definition and 671 Threads

In the notes attached here: https://www.physicsforums.com/showthread.php?p=3042019#post3042019 (apparently I can't attach the same thing in multiple threads?) I have quite a few problems with one of the proofs. In the proof of the proposition on p15, a) he says to note that \nu(0)=0. why...

So here is this thing that i really really can not agree with (regarding experiments)! What Bell's theory states (correct me, if i am wrong) and experiments with SPOT detector tend to prove is, that measurement of spin of one twin-light photon affects spin of other. Well - if we assume that then...

Homework Statement For a,b > 1 prove that: \int_{1}^{a} (1/t) dt + \int_{1}^{b} (1/t) dt = \int_{1}^{ab} (1/t) dt Homework Equations Hint: This can be written \int_{1}^{a} (1/t) dt = \int_{b}^{ab} (1/t) dt "Every partition P = {t0, ..., tn} of [1,a] gives rise to a partition P' = {bt0...

this might be answered already, but i didnt find a detailed proof... so here it goes: 1. an integer n is perfect if the sum of its divisors including 1 and itself is 2n. show that if 2^p-1 is a prime number, then n=2^(p-1) (2^p -1) is perfect. 2. show that 1+ 1/2 + 1/3 +... +1/n can never...

I am in the process of learning limits and there are a few things I would like to ask. 1) In order to apply the limit definition, you can't just have one point because there is no notion of 'approaching' a limit. I would like to play around with the limit concept by understanding some of the...

Homework Statement Let A be a skew-symmetric n x n matrix with entries in R. a) Prove that u^{T}Au=0 for every u E R^{n} b) Prove that I_{n} + A is an invertible matrix.Homework Equations A^{T} = -A The Attempt at a Solution a) u^{T}Au=0 Transpose both sides: (u^{T}Au)^{T} = 0^{T} The...

Homework Statement I'm trying to prove that "if R is an equivalence relation on a set A, prove that if s and t are elements of A then either [s] intersect [t] = empty set, or, [s]=[t]" Homework Equations The Attempt at a Solution I know that if you were to start trying to solve...

How to prove that a polynomial of degree 2 or 3 over a filed F is a prime polynomial if and only if the polynomial does not have a root in F? and i can't think of an example of polynomial of degree 4 over a field F that has no root in F but is not a prime polynomial. it says each...

Homework Statement Doing some studying for my midterm and came across these problems ... a) f : D \rightarrow R with a \leq f(x) \leq b for all c in D\{c}. Show that if lim_{x \rightarrow c} f(x) exist then a \leq lim_{x \rightarrow c} f(x) \leq b b) Same thing except we have g(x) \leq...

I have to do an induction proof that n!>n^2

Is there a "short" book on learning proofs? I realize that is probably an oxymoron :smile: I know that proofs take getting used to and lots of practice. However, I am in a bind here. I am an engineering student, so as you might imagine, I have almost never been asked to prove something...

Hi! I am having a lot of trouble with these problems: A-(An complement B)= AnB If A is a subset of B then AxC is a subset of BxC Ax(BuC)=(AxB)u(AxC) I don't get how to work them out. Can anyone help me please?

Hi everyone, please check the attachments for the problems. What i am looking for is not the help to answers. I've been desperately looking for relevant textbooks online that can help me out with proofs problems like that of the attachments. My professor does not provide a textbook, and his...

Hey all, I got a proposition I am supposed to prove by induction but am just a bit confused. The problem is as follows: Prove by the principle of mathematical induction that if m is a natural number, then for each natural number n, there exists an integer a greater or equal to zero such that...

Topology, Proofs, The word "Complement" Homework Statement I have a proof to do in which they use the word "complement". I am not sure what it means by that withing the context of the question. There is no glossary to the book and there is no mention of complement before this question...

Homework Statement -F is a continuous function on [0,1], so let ||f|| be the maximum value of |f| on [0,1] a. Prove that for any number c we have ||cf|| = |c|\ast||f|| b. Prove that ||f + g|| \leq ||f|| + ||g||. c. Prove that ||h - f|| \leq ||h - g|| + ||g - f|| Homework Equations Based...

Can someone help with this proof: G→(PVE), P→N, E→C, -(NVC) ㅏ-G This is what I have done so far 1 (1) G→(PVE) Assumption 2 (2) P→N Assumption 3 (3) E→C Assumption 4 (4) -(NVC) Assumption what do I do if here?

Homework Statement Use induction to prove this equation: F(n+k) = F(k)F(n+1) + F(k-1)F(n) Homework Equations F(0)=0 and F(1)=1 F(n)=F(n-1)+F(n-2) The Attempt at a Solution Base: n=0, k=1 F(1)=(1*1)+(0*0)=1 True for n=k k=k+1 F(2k+1) = F(k)F(k+2) + F(k-1)F(k+1)...

Hello fellow forum buddies :) Homework Statement a.) Prove that if a+b\sqrt{2} = c+d\sqrt{2} with a,b,c,d all in Q, then a = c and b = d. b.) Prove that a^2 - 2b^2 with a, b in Q is nonzero unless a=b=0 The Attempt at a Solution I really don't know where to start. Any tips...

I am doing some non-homework exercises in preparation for my midterm, and am struggling with the following proofs: First Prove {} is a subset of {}, where {} refers to an empty set My professor told me to do this by contradiction. So I assume that {} is not a subset of {}. That would imply...

Homework Statement The question says to find a proof for Cauchy's Inequality and then the Triangle Inequality. This is an elementary linear algebra class I'm doing, so I can't use inner products or anything. Homework Equations The Attempt at a Solution I got the proofs using algebra, but I'm...

hello everyone! I just started a course in real analysis and i must say that it is quite different from all the "engineering math" that i have taken before.I was wondering if anyone could give me tips or advice on how to get better at writing good proofs. Right now,we are using a book called...

Homework Statement "There is a very useful way of describing the points of the closed interval [a,b] (where we assume, as usual, that a < b) a. Consider the interval [0,b]. Prove that if x is in [0,b] then x = tb for some t with 0 <= t <= 1. What is the significance of the number t? What is...

I am having a hard time making head way on two problems related to the k-th prime and one about co-primes that I would really appreciate some help and/or direction! Prove that: (let pk be the k-th prime) and Regarding co-primes... is there any way to find a set of four numbers that are...

[SOLVED] Proofs for Dirac delta function/distribution Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations \delta(x) is defined as \delta(x)=\left\{\stackrel{0 for x \neq 0}{\infty for x=0} It has the properties...

Suppose you had some arbitrary function f : R^n \to R^p and x \in R^n. You want to know if it's continuous, so you do some epsilon-delta to find out for sure. However, only the most simple functions permit this without some extra restrictions. Consider f(x) = x^2. To show that |x - a| < \delta...

Analysis Help; proofs via axioms :) 1. The problem statement: Prove that for any real numbers a, b, c, (a+b+c)^2\leq3*(a^2 +b^2+c^2) 2. These are the axioms we are permitted to use: 01) Exactly one of these hold: a<b, a=b, or b<a 02) If a<b, and b<c, then a<c 03) If a<b, then...

Homework Statement *Sorry I could not get the math symbols to work properly so I did it by hand. I hope this isn't too much trouble. Prove: | sqrt( x ) - sqrt( y ) | <= | sqrt ( x - y ) | for x, y >= 0 Hint: Treat the cases x >= y and x <= y separately. I am new to proofs and we can't use...

I find myself switching my mind a lot when deciding whether to apply to aerospace engineering or applied math programs. One thing that will be a factor is how much proving of theorems is required in the applied math grad courses. Does anyone know how much proving of theorems is required in...

Homework Statement Prove that at least one of 2*10500 + 15 or 2*10500 + 16 is not a perfect square. Can you say specifically which one is not a perfect square? Consider the proof that √2 is irrational. Could you repeat the same proof for √3? What about √4? Homework Equations n/a...

Im thinking about taking a course in complex analysis. Furthermore, a course in proofs is recommended, but not required, as an intro into advanced math. I was wondering if anyone has the same recommendaton at their school or has anyone had it in the past. The main thing I am interested in is if...

Homework Statement Prove that lim x->3 of (x^{2}+x-5=7Homework Equations 0<x-c<\delta and |f(x)-L|<\epsilonThe Attempt at a Solution The preliminary analysis. The first equation in the relevant equations becomes 0<x-3<\delta And the second equation becomes |(x^{2}+x-5)-7|<\epsilon...

Hello, does anyone know where I can find a proof of the following identity? εijk εkmn = δim δjn − δin δjm

Hello. I was wondering if I should self study multivariable calculus or introduction to proofs? I am an entering high school senior (contrary to what my username might suggest), and I just took a Calc 2 class last spring. I can only do one or the other, and I don't know which one would be...

Hello guys, I don't know where else to post this but here goes. I'm going to be catching up on a looot of math this year. Unfortunately a lot of the math books that I'll be using only provide the answers to odd numbered questions. And the answers that they do provide a lot of the times "do...

At first glance these things seem so intuitive and familiar from other maths (like distribution) that I don't see how/where to start in proving them; while I know its probably quite simple. I understand what union and intersection are, but I'm unsure if multiplying two sets means a new set with...

Homework Statement Suppose the functions f and g have the following property: for all E > 0 and all x, if 0 < |x - 2| < sin((E^2)/9) + E, then |f(x) - 2| < E, if 0 < |x - 2| < E^2, then |g(x) - 4| < E. For each E > 0, find a d > 0 such that, for all x, i) if 0 < |x - 2| < d, then...

I really do not get proofs AT ALL. Stuff like this... "Prove that (n+1)2 \geq3n if n is a positive integer with n\leq4." Proof by exhaustion would be applied here.. what the book tells me. "Show that there are no solutions in integers x and y of x2+3y2=8." Then there's also...

Homework Statement a) Prove that \sqrt{3}, \sqrt{5}, \sqrt{6} are irrational. Hint: To treat \sqrt{3}, for example, use the fact that every integer is of the form 3n or 3n + 1 or 3n + 2. Why doesn't this proof work for \sqrt{4}? b) Prove that 2 ^ 1/3 and 3 ^ 1/3 are irrational. Homework...

I'm studying applied physics and I am currently in my second semester of the second year. I now have a probability and mathematical statistics course which is causing me a problem. Although I had lots of math prior to this course, none of it actually required writing proofs. Yet the spring...

If we feed all the existing mathematical axioms to a powerful computer, it should be able to give us all the proofs and theorems that can be derived using the axioms. Is there anything wrong with this logic?

Hi there, I have some exams later this month, and some of the previous exam questions are to prove a formula given another formula fx here with EM doppler shift: define ratio: r= f/ f0 using relativistic doppler frequency for EM: f = square root of: ((c+v) / (c-v)) * f0 Show: v/c =...

I need help in how to do this proof. A circle is given with diameter AB. pick any point C on the circle and drop a perpendicular from C to the given diameter at D. Find CD in terms of AD and BD.

I have the function f(x)=x^3/abs(x) I think that the following are all true: lim f(x)= inf. x->inf lim f(x)= 0 x-> 0+ lim f(x)=0 x-> 0- lim f(x)= -inf. x-> -inf and lim f(x)= dne. x-> 0 I'm not sure about the last one, because I thought that ususally when the limit...

I'm reading an article (http://arxiv.org/abs/gr-qc/0403075) which proves that a certain spacetime is geodesically complete. It does this by proving that the first derivatives fo all coordinates have finite bounds. My question is why this is enough. Is it just a simple ODE result? We know...

Homework Statement As a background to this...I have no experience with proofs at all. I did not take a formal geometry class in high school (took a shortened summer course that gave a VERY brief overview of proofs) and have not gotten to discrete math in university, so I really do not know how...

1. Let A be an m × n real matrix of rank r whose m rows are all pairwise distinct. Let s ≤ m, and let B be an s × n matrix obtained by choosing s distinct rows of A. Prove that rank(B) ≥ r + s − m. Solution: Assume that s is the largest amount of distinct rows of A. r = n-dimNul A...

so 0 < l x-a l < delta and l f(x)-L l < epsilon What I don't understand is how come deltas and epsilons can't be greater than or equal to their respective differences?

Homework Statement Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd. Let m be a positive integer. Show that a mod m = b mod m if a ≡ b(mod m) Homework Equations | means "divides," so a | b means "a divides b" or "b can be divided by a" mod gets the...

1. For any positive integer n, if 7n+4 is even, then n is even. 2.Sum of any two positive irrational numbers is irrational. 3. If m, d, and k are nonnegative integers with d=/=0 then (m+dk) mod d = m mod 4. For all real x, if x^2=x and x=/=1 then x=0 5. If n is an integer not divisible by 3...