Proofs Definition and 671 Threads

If m and n are positive integers, (mn)!=m!n! Prove or disprove. its so obviously true i can't prove it. anyone help? -also- Prove: The square root of a prime integer is an irrational number. any help?

Homework Statement F and G and H are vectors in D-3 a and b are real numbers Proof that F+G=G+F Proof that (F+G)+H=F+(G+H) Homework Equations The Attempt at a Solution I did put F=a,b,c and G=a1,b1,c1 and H=a2,b2,c2 and put that in. I just don´t know if that´s enough...

If a|(b+c) and gcd(b,c)=1, then gcd(a,b)=1=gcd(a,c) Suppose a|(b+c) and the gcd(a,b)=d. al=b+c and d|a and d|b. This implies a=dr and b=ds. drl=ds+c => drl-ds=c => d(rl-s)=c => d|c Since d|b, d|c and 1|b and 1|c, d must divide 1. Therefore d=1. By the same reasoning gcd(a,c)=1...

Hey all, I'm an absolute noob to number theory stuff and I've got this assignment to do with a few proofs. Homework Statement Proove that: i) if gcd(a,b) = c then gcd(a,a+b) = c ii) if gcd(a,b) = c and a = a'c and b = b'c then gcd(a',b') = 1 iii) if there exists r,s such that rx...

Homework Statement Are all types of mathematical arguments based on the following types of proofs? Types of proofs 1. Direct proof, P -> Q 2. Proof by contradiction, \neg Q -> \neg P 3. ~Ad absodium, P and \neg Q -> false statement (such as 0 = 1) I know the following types of...

Algebra Proofs! I have two questions just to help verify what I'm doing: Let R be a commutative ring with identity. Prove that R is an integral domain if and only if cancellation holds in R (that is, a no equal to 0 and ab=ac in R imply b=c) => Suppose cancellation holds: ab=0 -> ab=0a...

I think college is way tooo late to learn how to write mathematical proofs! Proof writing should begin at least either in elementary school or middle school. Proof writing is just as important to a students education as learning how to write sentences and learn how to combined those sentences to...

Hey people. I find myself getting through my course but currently with not as much understanding as I would like. We've got to some proofs and i either vaguely understand them or do not know how to prove them.Homework Statement The first would be to prove the Dimension theorem that. dimU +...

Hello all, I am stuck on some homework, basically I am stuck on the problems dealing with proofs. I am not asking for complete answers just any direction would be helpful. 1) I have to prove the Grötzsch graph is not 3-colorable (vertex can be colored in such a way that no edge shares 2...

Hi, I am doing some self-studying on the topic of functional analysis, specifically set theory at the moment. Suppose that we want to show that some set is denumerable. Is it required that we directly show the one-to-one correspondence between the elements of the set and the set of natural...

I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.

I don't know where to fit this question, but here goes. As an engineer should I be concerned a lot (or some) about proofs? Sure I know certain basic proofs anyone involved in math should know however, I have come across certain advanced proofs such as why certain methods of solving differential...

Two fairly simple proof problems. . . why aren't they simpler? :( Homework Statement Let A be an nxn matrix... If A is not invertible then there exists an nxn matrix B such that AB = 0, B != 0. (not equal to) Homework Equations None really. The Attempt at a Solution Obviously...

Cambridge press says available as of around 1 March, so in a couple of months. Samples are available of page proofs as they will, I gather, appear in the book. Here's the 3-page table of contents http://assets.cambridge.org/97805218/60451/toc/9780521860451_toc.pdf Here's an 11-page exerpt...

Hey all, I'm looking for a decent, (and preferably cheap) book, or books, on trigonometry. Something that proves some or all the trig equations we're expected to remember in high school stuff (most of which I've forgotten), but it should also leave room for my curiosity so I can prepare for...

Well, I have a take-home quiz and I need help with 6 geometry proofs. It is due tomorrow (Monday) and I honestly have no clue about any of it... here is the first question, please help me! Homework Statement Given: Angle ABG is congruent to Angle DEH Angle GBC is congruent to...

Got no clue .. need some clues

[SIZE="4"]My situation: I did good in high-school, learned algebra, functions, exp/log functions, limits/continuity, calculus, vectors, trigonometry, diff equations of 1st and 2nd order, and perhaps a few others things I left out. Came out with an A in math and physics, so far so good. Now in...

Homework Statement Suppose f >= 0, f is continuous on [a,b], and {integral from a to b} f(x)dx = 0. Prove that f(x) = 0 for all x in [a,b] Homework Equations The Attempt at a Solution Suppose there exists p in [a,b] s.t. f(p) > 0. Let epsilon = f(p) / 2 > 0. The...

Hey, I'm sure this must have been asked before, but I couldn't really find anything specific using the search tool; I'm a second year maths major and I love maths and would really like to pursue a career in mathematics. My problem is, often I can understand a proof (whether easily or not...

Homework Statement question 1: Define ~ on Z by a ~ b if and only if 3a + b is multiple of 4. question 2: Let A = {1,2,3,4,5,6} and let S = P(A) (the power set of A). For a,b \in S define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence...

Must a valid rule of inference always lead to a true conclusion?

Homework Statement 1. Prove that the sequence sqrt(n+1) - sqrt(n) converges to 0. 2. If sequence {an} is composed of real numbers and if lim as n goes to infinity of {a2n} = A and the limit as n goes to infinity of {a(2n-1)} = A, prove that {an} converges to 1. Is converse true? 3. Consider...

Let A,B,C,X,Y be subsets of E,and A' MEAN the compliment of A in E i.e A'=E-A,and A^B = A \cap B Then prove the following: a) (A^B^X)U(A^B^C^X^Y)U(A^X^A') = A^B^X b) (A^B^C)U(A' ^ B^C)U B' U C' = E Thanks

Homework Statement 1) Show by the use of vectors that the three altitudes of a triangle pass through the same point. 2) Show using vectos that the bisectors of the angles of a triangle pass through thr same point. 3)Find the distance from the point (1,0,-2) to the plane 3x-2y+z+1=0...

1) proe that for all non-negative real numbers x and y: xy(<or=)((x+y)/2)^2 2) prove that the sum of 2 prime numbers strictly greater than 2 is even 3) If n is a multiple of 3 then either n is odd or it is a multiple of six. I don't know how to start any of them. any hints would be v...

the function f(x) = 1 if x is rational f(x) = 0 if x is irrational is not continuous for all real numbers, c the function f(x) = x if x is rational f(x) = 0 if x is irrationa is continuous at x=0 and not continuous for all other real...

Geometry is arguably my weakest link in mathematics. The answers just don't "hit me" in geometry like some other sections of math do. When trying to prove something in a polygon, such as congruence of triangles made by segments etc. I find it difficult since the equal sides/angles aren't...

This is a famous proof that utilizes a common notion. Theorem. Limits are unique. let n>N_1 such that blah blah blah is less than epsilon over 2, let n>N_2 such that blah blah blah is less than epsilon over 2. For n> max{N_1,N_2}, blah blah blah < blah = epsilon...

hey everyone: Use a definition to work forward from each of the following statements. b. for functions f anf g the function f + g is convex, where f + g is the function whoes value at any point x is f(x) + g(x). Definition of a convex function...

I've also posted this in the Physics forum as it applies to some physical aspects as well. --- I want to know if I'm on the right track here. I'm asked to prove the following. a) \nabla \cdot (\vec{A} \times \vec{B}) = \vec{B} \cdot (\nabla \times \vec{A}) - \vec{A} \cdot (\nabla \times...

Homework Statement If x and y are arbitrary real numbers with x<y, prove that there is at least one real z satisfying x<z<y Homework Equations The Attempt at a Solution The problem arises from my inexperience in rigorously proving anything. If possible a general explanation of...

I'm not sure if it goes here or the section beyond calculus, so I'm just putting it here because it doesn't involve any calculus. Homework Statement Suppose that (a,b)=1 [Greatest Common Divisor=1] and (a,c)=1. Does (bc, a)=1? Homework Equations (a,b)=d=au+bv, where u and v are...

I have a 23 problem assignment due at the end of the week, and although I'm going to have a chance to talk to my teacher about the questions I have, I'd like to go ahead and get going on the problems. I've successfully completed 21 of them, but the last two are stumping me. I'm submitting them...

Hey everybody... I have a few quick questions concerning sets and functions for the experts... I've been trained in applied mathematics, so I'm not really used to this kind of formalism. 1. Can somebody look at my "proposed proof" of this elementary theorem for me? I have a feeling that it...

Philosophy of basic set theory proofs involving "or". Hey! I'm working through an Introduction to Analysis text, and I'm currently on the first chapter, which covers set theory. In one of the end-of-chapter problems, I'm asked to prove a basic theorem which leads to the following statement...

Hi, I finished calculus 1 in college this past year, and I was reviewing it in the summer to make sure I understand it and have a solid foundation for when continue taking math classes this upcoming year. My math has always been lacking a little from my high school past where I never paid...

My adviser asked me to study the first 50 pages of a book so I'm working the exercises. But they are all proofs, so I have no idea if I'm doing them correctly. I can't find any answers online, and even if I did, that would just tell me one way of proving it-- and there are, of course, many...

i've texed up three proofs in from elementary topology. can someone please check them? actually i'll just retype them here for convenience 8.2.5 Let f: X_{\tau} \rightarrow Y_{\nu} be continuous and injective. Also let Y_{\nu} be Hausdorff. Prove : X_{\tau} is Hausdorff...

Homework Statement For U(w)=sqrt(w), prove that U(pie(x)+(1-pie)y) > pie*U(x)+(1-pie)U(y) Homework Equations sqrt(x)=x^(1/2) The Attempt at a Solution I have: sqrt(pie(x)+(1-pie)y) > pie*sqrt(x)+(1-pie)sqrt(y) so... (pie(x)+(1-pie)y)^(1/2) > pie*(x)^1/2+(1-pie)(y)^1/2...

Hey Im trying to study abstract algebra, set theory and group theory, on my own. I have trouble understanding how to construct mathematical proofs though. Some of the things the excercises tells me to prove, seems so intuitively clear and obvious that I don't know what's left to prove. For...

I've been working on these problems and unfortunately i can't make heads or tails of these two. Any insight where to start the proof would be great. 1)Let A, B and C be sets. Show that if A~B⊆C, then A~C⊆B holds. What I got so far: Is it correct to state that A~B = A⋂B' and A~C = A⋂C'...

Would taking an intro to logic course help me prepare for the abstract proof writing skills that I'll need in upper division math?

In my self-study Calculus book I finished with the 'intuitive' definition of the limit and the text directed me to the 'formal' definition of the limit. After reading the section covering it a few times I think I comprehended the details of the rigorous rules dictating it - but obviously not...

Homework Statement I am having trouble understanding the proofs in Marion and Thorton [Newest Edition]. The section where he goes through proof of products in tensor notation. An example is page 26 example 1.6. I don't get the switching of the indices on the very last part. Also can someone...

I'm trying to understand \epsilon-\delta proofs, but I'm having some trouble. For example, if we want to prove that \lim_{x\rightarrow2}x^3=8, starting from |x^3-8| we get to something like |x-2||x^2+2x+4| And this is what confuses me: we conjecture that |x-2|<1, then |x|<3, so we get...

http://www.themathlab.com/geometry/funnyproofs.htm

[SOLVED] Couple of Proofs (Regular Induction / Well Ordering) Hi there everyone, I've been having a bit of trouble of solving these questions, so any help would be greatly appreciated: Homework Statement 1: Prove, via regular induction, that it is possible to draw a line-segment of length...

Hi First of all, I would like to mention that I can do proofs that involve algebraic manipulations (in a field i.e.) pretty well, or proofs that involve epsilon-delta arguments or mathematical induction. However, at the moment I'm reading "Principles of mathematical analysis" and I have a hard...

I searched around and I found some books on how to write proofs. There are so many of them that got good review and I have no idea which to choose. Here are some books I am considering: How to Solve It, by Polya An Introduction For Mathematical Reasoning, by Eccles The Nuts and Bolts of...