Proofs Definition and 671 Threads

I am writing my first paper in applied mathematics.I would like to know how important is it to write a analytical proof for the numerical solutions arrived?I always thought these sort of things were left to the 'pure mathematicians' and one didn't need to bother.As a engineer,I was always used...

Hi, I'd be grateful if someone could tell me whether these proofs I've done are correct or not. Thanks in advanced. Let V be an n-dimensional vector space over \mathbb{R} Prove that V contains a subspace of dimension r for each r such that 0 \leq r \leq n Since V is n-dimensional...

I'm having a lot of difficulty with proofs. I can understand them when I read them, but when asked to prove things myself, I usually fall flat on my face. How important are proofs for physics? Do I really need an intimate understand of the mathematics, or would that be irrelevant? I was...

Homework Statement (a) The ratio v/c is very often denoted by the single symbol β. Show that if β<<1, the following are valid through terms of order β^2 E = mc^2 + (mv^2)/2 = (mc^2)[1+(β^2)/2] K = (mv^2)/2 = (mc^2)[(β^2)/2] pc = mvc = m(c^2)β γ = 1+(β^2)/2 (b) Show that if γ = ε^-1...

Homework Statement When constructing an Epsilon Delta proof, why do we need to make a stipulation? For example, in most proofs for limits of quadratic functions, it is stipulated, for example, that δ≤1. Why is this needed anyway? This is my thought process for a quadratic: Prove that lim(x...

There are certain formulas for which only inductive proofs are known. But since we need to know the formula first to prove it using mathematical induction, how do they get the formula in the first place? Here is an example: - Euler's formula in graph theory states that v-e+f=2 for all planar...

I feel the question i am going to ask it is one of the most important question ,if not the most important,in Mathematics. And i may add if answered correctly a lot of misunderstanding and useless arguing can be avoided. So here is the question: What are the mathematical means or theories that...

Q1 Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear. Q2 AB and CD are two parallel chords of a...

Homework Statement a) Let H be a normal subgroup of G. If the index of H in G is n, show that y^n \in H for all y \in G. b) Let \varphi : G \rightarrow G' be a homomorphism and suppose that x \in G has order n. Prove that the order of \varphi(x) (in the group G') divides n. (Suggestion: Use...

Where does one attain the skill/ability (skill vs. ability is a good question in itself) to do proofs? By "do proofs" I mean prove existing theorems. For instance I am really no good with ε-δ proofs. The concept is so easy, but when I have to prove something using ε-δ I either have no idea what...

Homework Statement For n ∈ Z+ prove by contrapositive that if 2n3 + 3n2 + 4n + 5 is odd then n is even. Homework Equations The Attempt at a Solution If n is odd then ( 2n³ + 3n² + 4n + 5 ) is even. By definition, a number n is odd if n = 2k + 1 for some integer k. A number...

Homework Statement lim (x,y) -> (0,0) xy/sqrt(x^2+y^2) = 0 The Attempt at a Solution my understanding of my actual goal here is kind of poor given ε>0 there exist ∂>0 s.t. 0 < sqrt(x^2 + y^2) < ∂ then 0<|f(x,y) - L| < ε | xy/sqrt(x^2 + y^2) - 0 | < ε (xy * sqrt(x^2 + y^2)) /...

Homework Statement Proof that the following statements are all equivalent. First assume that none of the vectors are zero vectors. Then prove it in the degenerate case, where the vectors are zero vectors. 1) u = kv where k is a scalar. 2) u \times v = 0 3) u \cdot v = ||u|| ||v|| 4)...

Homework Statement Let x \in ℝ Prove that if 3x^{4}+1≤x^{7}+x^{3}, then x > 0 Homework Equations None The Attempt at a Solution Assume 3x^{4}+1≤x^{7}+x^{3} then 0 ≤ -3x^{4}-1≤x^{7}+x^{3} Then I assumed that each was greater than or equal to 0, which I thought gave the desired...

Hi, i need help with 2 proofs based off of floor and ceiling. 1.)F[FONT=Verdana]or any real number x, if x is not an integer, then floor(x)[FONT=Verdana] + floor(-x) =- 1.2.[FONT=CMR10]For all real numbers [FONT=CMMI10]x, floor(floor([FONT=CMSY10]x/2)/2) [FONT=CMR10]= floor([FONT=CMSY10]x/4)...

I'm a sophomore at Rensselaer Polytechnic Institute and I'm taking MATH 4600 which is Advanced Calculus. I love the class and it is very interesting, we're taking what we learned in Multivariable Calculus, but just at a much higher level. However, my teacher does a lot of proofs behind why...

Hello there, I am extremely new to mathematical analysis and do not have an idea how to prove the following questions. Could you please give me a hand and show me a way? Let At , t ∈ T, be a family of sets, and let X be a set. Prove the identities...

Homework Statement hopefully the writing is readable: http://i.imgur.com/VJ8vN.jpg All three if possible. Homework Equations none The Attempt at a Solution To be completely honest, I missed that whole week of lectures due to personal problems and I've had no chance to talk to an...

Homework Statement I've got two questions out of my textbook. I'll list both of them and my attempts below. (1) Suppose : a, b, c\in Z, a|c \space \wedge \space b|c.\spaceIf a and b are relatively prime, show ab|c. Show by example that if a and b are not relatively prime then ab does not...

I'm going to construct an ordered set, and I'd like to ask some questions about it; and in particular consider coding problems about this set and sets in general (Turing tape encoding). Start with: A={ } And, allow a mutable temporary set, initialized with: T={ } and an iterator: set n=0 For...

Homework Statement Prove that if 0 < a < b, then a < √ab < (a + b)/2 < b Homework Equations To prove this use the 12 properties of numbers (commutativity, trichotomy law, associativity, etc...). The Attempt at a Solution The main problem is I don't know if I need to define the...

Homework Statement I am stuck at this point where I have to prove that the kronecker delta is isotropic tensor. Homework Equations δij=δji The Attempt at a Solution I know that to prove this I have to show that under coordinate transfor mation it does not change..but it's a bit...

Homework Statement Homework Equations The Attempt at a Solution -(y, x) = -(YX-XY) = XY-YX Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)...

Homework Statement Lim x→a of f(x) = c (Where c is a constant) Homework Equations The Attempt at a Solution I have no idea. I am able to do these if I can manipulate fx-L to equal x-a but I am having trouble with this one. Please help me!

Homework Statement Prove the following limits using delta-epsilon definition (a)\mathop {\lim }\limits_{x \to 5{}^ - } \sqrt[4]{{5 - x}} = 0 (b)\mathop {\lim }\limits_{x \to 2} ({x^4} - 1) = 15 (c)\mathop {\lim }\limits_{x \to - 1} \frac{{{x^2} - 2x}}{{x + 2}} = 3 Homework Equations...

Hey all, So I'm just starting a course in linear algebra, but I don't have much experience with proofs. This problem has been giving me some difficulty. So we have a scalar "a" and vector x. V is a linear space, and x is contained in V. I have to show that if ax=0, where 0 is the zero...

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P[B]} appeared and it's just not sitting right with me. I know that...

Homework Statement Hi, I'm taking a mathematical proofs class and I'm having trouble formatting my proofs correctly. We haven't done any proofs in class yet, but some simple proofs are due in this week's homework assignment. I've tried using the internet to help me, but all the hits that I get...

Hi everyone! I'm a new user of this forum! I was interested in learning to make proofs of the various theorems. Is there a schematical way to make the proofs ? Where should i start ? And what are the statement for my proofs that are absolutely true so that i can base my proof on ? Is there...

Hey all, I am trying to get a head start on Linear Algebra before i start taking classes in a couple weeks. I am about to go into my second year undergraduate and all i have behind my belt is calculus (single varialbe, multivariable, and vector analysis (curl, divergence, etc)). I am...

Hello everyone. I'm a first time poster, but a long time lurker. I don't have a degree in physics, but I have always held the discipline and all its branches, near to my heart. A little background on the question. I got into an argument with a friend of mine about faith in religion and faith...

In online maths fora we often see posts like the first post in thttp://www.mathhelpboards.com/f15/book-recommendations-proofs-1649/#post7709 from kanderson. When I was in secondary education and then an undergraduate we were never taught about poofs, rather we saw them and produced our own...

I want a good book with an introduction to either graduate or undergraduate mathematics that has excercises and clear explanations.

Hey Physicsforums, This is something I run into quite a bit in my study of mathematics. Proofs are very important - that much is true. However, there are many instances when I don't need a proof to understand a concept; I just understand it. For example, I don't need...

I am doing exercises form Velleman's How to Prove It Homework Statement 1. Suppose a and b are real numbers. Prove that if a < b < 0 then a^2 > b^2. 2. Suppose a and b are real numbers. Prove that if 0 < a < b then 1/b < 1/a. 3. Suppose a and b are real numbers. Prove that if a < b...

Both algebra and analysis are pretty much all about proofs...but a prof told me the proofs in algebra are very different from those of analysis. How are they different? Any input appreciated.

Can anyone help me confirm if I have solved this correctly? Many thanks. Homework Statement Q. 9^n-5^n is divisible by 4, for n\in\mathbb{N}_0 The Attempt at a Solution Step 1: For n=1... 9^1-5^1=4, which can be divided by 4. Therefore, n=1 is true... Step 2: For n=k...

Is it necessary to know the proofs of all the propositions in Euclid's elements? Or one can directly jump to euclidean and precollege geometry, of course he/she will have knowledge of propositions( just the statements and all that) but not the proofs. Reply Quickly.

I need some advice on proofs in my calculus/analysis course. I just wrote a test and it didn't go anywhere near according to plan. My problem keeps on revolving around how to do proofs of certain claims. Now the proofs for these claims on the test at least were proofs for the most part straight...

I hope this is in the right section, otherwise please move it. This might be a long post and I hope someone will give it a shot. It is about books but not really a comparison between them. I will give some background first, so you might skip to the end (- Books * -) if you are only interested in...

Here's a quick question concerning writing clearly in proofs. I am revising and refining some of my proofs [this is for a self-study], and I across a problem where I had to prove that f: G->G defined by f(x)=axa-1 is a automorphism. To show it has the homomorphism property, I had to do some...

Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer. I proved it like this. I think its right but I am not able to word it correctly. Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-2=-2. Since 0 is an integer, 3n-6 is even. How can I learn to word this correctly because I am having some...

Homework Statement Let nεZ,Prove that 1-n^2>0, then 3n-2 is an even integer. Homework Equations The Attempt at a Solution I proved it like this. I think its right but I am not able to word it correctly. Since 1-n^2>0 therefore n=0. Then 3n-6=3(0)-6=-6. Since 0 is an integer, 3n-6 is even...

Hi, I was wondering if you can suggest good books on the techniques for mathematical proofs. I know this is quite a simple matter but I would be glad if you could suggest me with greats books for teaching proofs. More often than not I used the direct method and induction to prove problems in...

Lately, I have been experiencing a sort of anxiety over not understanding some of these proofs in my calculus textbook. I just finished a calculus I course, and we did not spend any time learning them; so, I thought, since it is summer time now, I would go back over and try to learn those...

Hello all, I was wondering if someone has ever found a purely algebraic proof for the addition/subtraction theorems of trigonometry, mainly sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Given a right triangle: Let x be one of the perpendicular legs and let the other leg be composed of two parts, y1...

Hello, I would like to check my arguments for this problem. Homework Statement Consider the relation R = \{(x,y) \in \mathbb{R} \times \mathbb{R}: x-y \in \mathbb{Z}\} on \mathbb{R} . Prove that this relation is symmetric, reflexive, and transitive. Homework Equations Supposing a relation...

Hrm... Congruence Proofs. Don't remember the "rules" Homework Statement Take equals sign as congruence or equals based on context, please. Itex does not work in Opera. Prove that for all n, 8^n = 1 (mod 7) Homework Equations The Attempt at a Solution This will be a proof by...

Homework Statement http://gyazo.com/94783c14f2d2d05e62e479ab33c73830 Homework Equations I know the dot product and cross product, but even for the first one I don't see how either helps. The Attempt at a Solution 1. the gradient of the 2 scalars multiplied together (not crossed...

Hey, I'm new to the forum so I'm not sure if I posted this in the right section. I'm taking Intro to Logic and I'm having some problems. Proofs: Construct proofs for each of the following symbolic arguments. Commas are used to mark the breaks between premises. (Each proof can be completed in...