Proofs Definition and 699 Threads

Prove that a sequence of uniformly convergent bounded functions is uniformly bounded. Attempt at proof: So first we observe the following: ||fn||\leqMn. Each function is bounded. Also, |fn-f|\leq\epsilon for all n \geq N. First off, we observe that for finitely many fn's, we have them...

Homework Statement Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants. Homework Equations Δ = gradient vector 1) Δ(u/v) = vΔu - uΔv / v^2 2) Δu^n = nu^(n-1)Δu...

Please Help! proofs using contrapositive or contradiction Homework Statement Prove using contrapositive or contradiction: For all r,s∈R,if r and s are positive,then √r+ √s≠ √(r+s)

I'm not using the suggested formatting because my question doesn't fit it. If this belongs elsewhere, I apologize for posting it here. I am currently in Calc II and we are starting to prove certain things. I found out that I really enjoy this and want to do a few proofs a week just for fun...

I'm not quite sure if this is the correct subforum. I was wondering if anybody knew where I could find some decent real analysis notes or lectures online, specifically on the formal definition of a limit. My prof is great, I just missed the class and the textbook and notes aren't quite making...

I was accepted into a top tier Ph.D. Operations Research program. I have six months to prepare independently on my own (at home). Everybody told me real analysis is the first thing I should look at (which makes sense, because I don't have proof experience). Can you please recommend me a book...

Looking for a little advice regarding proving things in mathematical way. I am a physics major currently taking a math methods course where we are asked to prove things, basically for the time in my schooling career. Sometimes I have trouble formulating a mathematically rigorous way of...

Any resources to learn how to do proofs or view abstract math better in linear algebra? A lot of time when I read the solution to proof questions, I don't even see how that proves the statement. The way they are written seems unintuitive. This is my first abstract math course. I've never had...

Hi, Could you clarify the relationship between proofs that use ≤ and those that use <? For example, if it's already proven that "abs(b) ≤ a if and only if -a≤ b≤a" can we say this implies that "abs(b) < a if and only if -a< b<a"? It seems that since the first statement holds for all abs(b)...

URGENT Field Proofs help. I need to prove the following: 1) Prove that if x, y are elements of a field, and X x
Y = 0 then either x = 0 or y = 0 . Write a detailed solution. and mention which of the eld axioms you are using. 2) Let F be a field in which 1 + 1 = 0 . Prove that for any...

Hi I'm a math layman so please be simple and straightforward. Thanks. Are axioms/postulates in any field always so self-evident that they don't need any proofs? I could say '1+1=2' is an axiom, am I allowed to say this, or are there some requirements for an axiom to qualify as one? Could...

Homework Statement [PLAIN]http://img641.imageshack.us/img641/2494/mathg.png I've worked through it and at the 1st step I get: (1/-e+1)<x<(1/e+1) How do they have (1/e+1)<x<(1/-e+1)? Do you switch the signs of an inequality when you take the inverse of both sides?

Homework Statement a.) Given \delta_n=\frac{ne^{-{n^2}{x^2}}}{\pi} Show: x{\frac{d}{dt}\delta_n}=-\delta_n b.) For the finite interval (\pi,-\pi) expand the dirac delta function \delta(x-t) in sines and cosines, sinnx, cosnx, n=1,2,3... They are not orthogonal, they are normalized to...

Hi all, I have taken Calc III, Linear Algebra (Bretscher's book), and an ODE class, which have all been mostly computational. I plan on taking upper level math courses such as abstract algebra and analysis, and my understanding is that the latter are proof based rather than computational. Are...

A Free Book "Proofs and Types" http://www.mpi-sws.org/~dreyer/tor/papers/girard.pdf Proofs and Types Jean-Yves Girard Translated and with appendices by: Paul Taylor Yves Lafont Cambridge University Press New York Melbourne New Rochelle Sydney Published by the Press Syndicate of...

It looks like memorization plays a key component of recognizing/remembering when to use certain "rewriting" tricks to get the desired result in the string of deduction. I had to think for a minute about some of the equations involving absolute values...

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...

Making use of the fact that dH = CpdT + (V - T(\deltaV/\deltaT)P ) dP is an exact differential expression, show that: (\deltaCp/\deltaP)T = -T(\delta2V/\deltaT2)P What is the result of application of this equation to an ideal gas?So I literally have no idea what is going on. I've asked for help...

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...

Homework Statement l is an infintesimal material element of length. show that: Dl/Dt = l dot grad u where l is a smallelement that exists in the velocity field u. Consider its position at time t and t+dt The Attempt at a Solution have l(x,t) where x is representing all...

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...