Proofs Definition and 699 Threads

Homework Statement I'm currently in first year linear algebra... I'm doing quite well, there's just one area of trouble-- proofs. For example: Suppose u.v = u.w, does it follow that v = w? Prove your generalization. Prove that u is orthogonal to v - proju(v) for all vectors u and v in R^n...

Hello. I have an upcoming exam for my math course and I am aware that much of it will revolve around Epsilon-Delta proofs. My understanding of them is good enough to prove most limits, but I would be more comfortable being able to answer anything that is thrown at me on this test :confused:. I...

First, thanks for all the help so far everyone! vectors a and b exist in the x,y plane and make angles (alpha) and (beta) with x. (Ill use A as alpha and B as beta) prove: cos (A-B) = cos(A)cos(B)+sin(A)sin(B) prove: sin (A-B) = sin(A)cos(B) - cos(A)sin(B) I think there is some...

Hello all, I'm having a hard time trying to prove a few things. I'm looking for a little help because I cannot seem to grasp the concept of proofs and what constitutes a valid proof and if my proof is wrong, correcting it. I have a proof done and if anyone could "critique" it I would be...

...involving Matrix Multiplication... I think it is mainly the notation that is killing me here...but it is killing me. Problem: Check parts (2) and (3) of theorem (1.3.18) which says: 1. A(BC)=(AB)C 2. A(B+C)=AB+AC 3. (A+B)C=AC+BC The author led the way on part one with this proof: Let AB=D...

Homework Statement Prove or give a counterexample to each statement. (S ∩ T) ∪ U = S ∩ (T ∪ U) The Attempt at a Solution If I proved by the contrapositive S (T ∩ U) ≠ (S ∩ T) ∪ U where would I go from there. How do I find the contrapositive with the unions and...

I have no luck with proofs... Prove that B_{r} ((x_{0}, y_{0})) = {(x,y) : || (x,y) - (x_{0}, y_{0})|| < r} is an open set in R. Now I know that to be an open set if and only if each of its points is an interior point and if it contains no boundary points. I would consider trying to prove...

It's hard to find the proofs of these theorems. Please help me... Thanks! Theorem 1: Let V be a vector space over GF(q). If dim(V)=k, then V has \frac{1}{k!} \prod^{k-1}_{i=0} (q^{k}-q^{i}) different bases. Theorem 2: Let S be a subset of F^{n}_{q}, then we have dim(<S>)+dim(S^{\bot})=n.

Can the epsilon associated with f(x) be a function of x? i.e epsilon = delta * (x-2)^2 valid?

I'm planning on taking a limits and infinite series course soon and was wondering what book(s) I could get off Amazon that would make the process a little less painless when it comes to proofs? Quantifiers, those sort of things, I have no idea about any of it and I'm taking a pre-limits class...

im looking for a book that shows the fundamentals of proofs cause I am starting and i want to start with the basics. thanks

L1-, L2-, Linfty-Norm Proofs - Please Help! Homework Statement Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers. Homework Equations ||x||2 is defined here: http://mathworld.wolfram.com/L2-Norm.html ||x||1 is...

1) Prove that f defined by f(x)= e^(-1/|x|), x=/=0, f(x)= 0, x=0 is differentiable at 0. [I used the definition of derivative f'(0)=lim [f(0+h)-f(0)] / h = lim [e^(-1/|h|) / h] h->0 h->0 and I am stuck here and unable to proceed...] 2) Suppose lim...

I just stare at difficult proofs. I truly do not understand induction. Like if I was to prove Fermat's Little Theorem, I wouldn't know where to start. And I have my final exam next week and I don't know how to study since its all proofs. And if you say do a lot of problems , what happens if I'm...

Below is a list of notes on mathematical proofs. The notes are directed at beginners who want to learn how to write mathematical proofs.PROOF TECHNIQUES 1) Introduction to mathematical arguments (by Michael Hutchings) http://math.berkeley.edu/~hutching/teach/113/proofs.pdf 2) How to Write...

i need to prove that if f and and g are analytic functions in (-a,a) then so is fg. well basically i need to find the radius of convergence of fg, which its coefficient is: c_n=\sum_{i=0}^{n} b_i*a_{n-i}, by using cauchy hadamard theorom for finding the radius of convergence, and to show that...

Homework Statement Let D be a subset of C and D is open. Suppose a is in D and f:D\{a} -> C is analytic and injective. Prove the following statements: a) f has in a, a non-essential singularity. b) If f has a pole in a, then it is a pole of order 1. c) If f has a removable singularity...

Homework Statement Prove or disprove the following: (A is a nxn square matrix) a) The vector b is in R^n and all its elements are even integers. If all the elements of the A are integers and det(A) = 2, then the equation Ax = b has a solution with only integer elements b) If n is odd and...

When solving a problem, the last thing you want to do is look at the solution. When you're trying to prove a theorem, axiom or whatever, is looking at a proof something that would impede your learning? To me it seems that the answer is yes. Looking at a proof removes the thinking process so...

Homework Statement Prove that if n is an odd positive integer, then n^2\,\equiv\,1\,\left(mod\,8\right). Homework Equations Theorem: a\,\equiv\,b\left(mod\,m\right) if and only if a\,mod\,m\,=\,b\,mod\,m The Attempt at a Solution Using the theorem above: a\,=\,n^2 b\,=\,1,\,m\,=\,8...

How do I go about finding alternative proofs? I wrote an alternative proof to a theorem including its converse, so I'd like to publish it if it does not yet exist. So far, I just looked into 10 different textbooks that had the theorem. I don't really know much else to do. So far so good...

The following theorems are usually left unproved in calculus, for no good reason. See what you think. 2250: Elementary proofs of big theorems The first theoretical result is the Intermediate Value Theorem (IVT) for continuous functions on an interval. Theorem: If f is continuous on then...

Any suggestion on how to improve your reading fluency with proofs of theorems? It's frustrating to spend over 1 hour to read a proof of a theorem that is under 1 page long (or not understanding the proof altogether). Even when every subtopic within a proof is already known, I find that...

Are truth tables acceptable forms of proving the equality and inequality between sets. For example, A U (B^C) = (AUB) ^(AUC) A B C AU(B^C) (AUB)^(AUC) F F F F F F F T F F F T F F F F T T T T T F F T T T F T T T T T F T T

Homework Statement 1. Prove that if n is an even positive integer, then n³-4n is always divisible by 48. 2. Prove taht the square of an odd integer is always of the form 8k+1, where k is an integer. 3. Observe that the last two digits of 7² are 49, the last two digits of 7³ are 43...

Life is short, and I know I can never experience all of mathematics. So I want to construct a plan to see as many of the unique proofs (across the various disciplines) as possible. (Independently, I'll also proceed to learn as much as possible in depth as well). Reading Munkres'...

Disclaimer: I might have some problems getting my LaTeX code to work properly so please bear with me while I figure out how to properly use the forum software. Homework Statement The exercise is to prove the following statements. Suppose that f:X \rightarrow Y, the following statement is...

so, I am in my first upper level math course beyond required calculus and the introductory linear algebra class. I don't know if it's just a great jump or if I slept through something, but suddenly everything is all about doing proofs. I'm okay with that, and I think it's fabulous because proofs...

I know I posted a similar question before but it was moved to the Academic and Career Guidance section and so I got answers from many non-relativists who answered no because they weren't into theoretical physics. So let me be more specific here. Would someone specializing in general...

Hey, i was reading through the proof of limit of sum rule in my textbook, and I've ran across somethin i can't understamd. in the proof th textbook uses the triangle inequality: |(f(x) - L) + (g(x)-M)} < e <= |(f(x)-L)|+|(g(x)-M| and then used the latter part in the rest of the...

Geometry Proofs.. Help! Please please someone help me! :eek: I have a Geometry Exam on Monday and I don't understand proofs one bit :cry: ! If someone could help me with a few proofs that would be so awesome!

I'm a mathematics specialist with interest in general relativity, and would later like to learn quantum field theory and superstring theory. Of course this requires learning mountains of mathematics that I haven't even learned yet because I spend 80% of my studies doing math proofs. Doing...

I'm a math graduate student, but also have great interest in computer capabilities. Chess players once thought that a machine cannot beat the world's best chess players because they cannot plan like humans despite their calculational power. Nowadays, computers are consistently beating the...

I've noticed a lot of mathematics on this forum revovles around proofs, but have not really come across any in depth proofs as such and so am unfamilliar with much of the topics discussed here, and in fact some I can't really follow. I got to thinking though at which point does it become...

Trying to press on through Epsilon-Delta proofs of limits (for more than one variable) and yet there's only one example I've found thus far of even a multi-variable Epsilon-Delta proof. Would it be possible for someone to solve the Epsilon-Delta proof of the limit: (xy^2)/(x^2+y^2). Note...

I am looking for some good websites that have proofs involving parallelograms and rhombus'? preferably in statement and reasons format any help would be appreciated. thank you

I know this is a simple part of Quantum Mechanics, but I seem to be having trouble with it, I'm not sure if my math is just wrong or if I'm applying it wrong. The questions that I have are: Prove the following for arbitrary operators A,B and C: (hint-no tricks, just write them out in...

I was wondering i really want to study formal math with proofs etc. Are there any good books out there?

Hey, I need help with a couple of questions in my analysis calc and proof class. Thanks in advance! Prove that S = { n−1 |n ∈ N} is bounded above and that its supremumn is equal to 1. Use the Intermediate Value Theorem to show that the polynomial x4 + x3 − 9 has at least two...

I m having trouble with a couple group theory proofs. I just have no clue how to start. If u could put me on the right path that would be great. first prove of disprove that if every subgroup of a group G is cyclic, then G is cyclic. and second prove or disprove that every group X of...

1) Find two matrices A and B where Rank [AB]≠Rank(BA) 2) Find a matrix A where Rref(A)≠Rref(A^T) where T is the transpose 3) Find X given that B is invertible if BXB^-1 –A=I_n (identity matrix) 4) Prove that [Ab_1 Ab_2 Ab_3] is linearly dependent given that {b1 b2 b3} is linearly...

I'm a current physics major and considering whether I should minor or double major in math as well. Since I've heard that physics majors need to take upper-division linear algebra and analysis, and I'm currently taking a mulitvariable calculus course, should I be spending time trying to...

Can't start: (log_{a}b)(log_{b}a) =1

i need to be able to prove that an nxn matrix with two identical columns cannot be invertible. I know that if the columns of the matrix are linearly independent then the matrix is invertible. Could some please give me a hint on how to do this proof because i really don't know where to start...

Hi, Why is it, that when ever epsilon-delta proofs are done, once delta is found in terms of epsilon, it is reinputed through again? Is there any point to this really?

I'm reading Introduction to Mathematical Logic gy by Vilnis Detlovs and Karlis Podnieks, and I'm confused about proofs. In the book, it says that to prove directly you should find ways to substitute the hypoethesis formula(s) into one of the axiom schemas so that other formulas will be...

I need to prove that <acb is equal to one of the other interior angles of triangle abc. help when pic uploads

I get the theory of special relativity, it is the logical conclusion drawn from the two facts that: a) the laws of physics are the same in all reference frames b) the speed of light is constant in all reference frames what I don't get is why einstein thought the speed of light was constant...

Here is the question. I have to prove it. Prove that the square of an odd integer is always of the form 8k+1, which k is an integer. Now I do not know how to start it. But this is what I came up with. odd integer= 2k+1 therefore the square of an odd integer (2k+1)^2 i have used...

Show that for a single particle with constant mass the equation of motion implies the following differential equation for the kinetic energy: {dT\over dt} = \vec F \cdot \vec v while if the mass varies with time the corresponding equation is {d(mT)\over dt} = \vec F \cdot \vec p Proof...