Proofs Definition and 671 Threads

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?

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...

Are 2b, 2c, and 2d correct? The last part of 2d I am getting stuck. http://www.artofproblemsolving.com/Forum/weblog.php?w=564 note: you can comment on the site as a guest Thanks

Lets say you are given a bunch of statements and you need to ask some questions to prove them: (a) How do you show that a set is a subset of another set. I said to show that x\in A and x\in B [/tex]. What else can you do to show what A\subset B ? Could you assume from the following: If...

I have read that a valid method for prooving a statement is to assume the opposite and show a contradiction. This tells me the assumption is an "either or". If this is not true, then that must be. Is this always valid?

People usually say that pictures tell more than 1000 words. Is that still true in mathematics...? I think so. Let me first say what i mean by 'visual proof'. Let's say we have an identity. To prove it's true one may write from a line to more than one page. But what if one was able to write only...

I'll be starting university in just over a month. The school I'm going to has advanced section classes that basically cover the first year math classes (Algebra and Calculus) in a more rigorous fashion than what is usually offered to first year math students. I am interested in taking part of...

Hi Im new in this Forum. I am from Switzerland, in the first year of Physics at University. Please forgive some mistakes I might will make in english I read a little bit in advance for the next years about the SRT and its relation to other fields of study. Basically I wanted to know...

First of all if you read this and the latex is all messed upp I am probably working on getting it right so please be patient till I get it right. No need to post a comment that it doesn't work. Thanks :wink: I haven't taken a pure maths class in over 2,5 years so I can hardly remember how to...

Hello. I've been reading through Friebderg's Linear Algebra and doing some of the problem sets. I can do the problems with little problem, but I want to make sure my proofs are okay looking. These are pretty basic though. I'm pretty sure I got the first one, just want to make sure that's right...

Hello. I'm self-studying Linear Algebra and I'm thoroughly enjoying the subject of Vector Spaces. While reading through the text, I came upon a theorem that states "Let S_1 and S_2 be finite subsets of a vecotr space and let S_1 be a subset of S_2 . Then If S_1 is linearly dependent then...

If n \geq 1 and f(a) = 0 for some real a , then f(x) = (x-a)h(x) , where h is a polynomial of degree n-1 . So: f(a) = \sum_{k=0}^{n} c_{k}a^{k} = c_{0} + c_{1}a + c_{2}a^{2} + ... + c_{n}a^{n} = 0 . In a hint it says to consider p(x) = f(x+a) . So I expanded that and got...

Prove that 1^{3} + 2^{3} + 3^{3} + ... + n^{3} = (1 + 2 + 3 + ... + n)^{2} . So for n =1 1^{3} = 1^{2} . For n = k , 1^{3} + 2^{3} + 3^{3} + ...+ k^{3} = (1+2+3+...+ k )^{2} . For n = k+1 , 1^{3} + 2^{3} + 3^{3} +...+ k^{3} + (k+1)^{3} = (1+2+3+..+ (k+1))^{2} . So do I then do this...

Prove that each of the following sets is measurable, and has zero area: (a) a set consisting of a single point (b) a set consisting of a finite number of points in a plane (c) the union of a finite collection of line segments in a plane (a) To prove that a set is measurable you have to say: Let...

"smallest set" proofs From time to time I've seen proofs (to disprove some assertion) which are based on claiming that if the assertion P holds for some sets, there must be some set S which is the smallest set for which P holds, and then showing that if P holds for a set of size |n| it must...

I'm having some trouble with one particular geometry proof: From that I've drawn the following: http://img96.imageshack.us/img96/139/circle9we.gif \angle ADB = \angle CED (as \angle ADB and \angle CED are alternant sements) \angle CBD = 180 - \angle CED (1) (as they are opposite angles in...

I don't get any of this and the textbook doesn't help that much either. I was wondering if someone could help me wiht this one question: Prove that every positive integer, ending in 5 creates a number that when squared, ends in 25.

Im doing a mathematical proof in my discrete class and i was wondering if you guys had any sort of interesting ideas for me to cover, the criteria is that it is beyond the grade 12 level. They must be either relevant or obscure. ANy ideas...?

I am having a nightmare trying to prove things in set theory. One of my homework problems is to prove that: Dom(R U S) = Dom(R) U Dom(S) but i have no idea how to really do this. my teacher never went over this stuff! IT'S SO AGGRAVATING! can anyone reference a good site or book on...

As I discussed with a friend's cousin, who is completing a Ph.D. in Astrophysics, he said that the ONLY evidence for the Big Bang was the seen redshift from the other galaxies around. Is he right, or is he wrong? If he is right, how can we base cosmology over a single, 'weak' proof like...

For proofs, can we take for granted that an even number x an odd number is even? I'm supposed to prove that for ever natural number, n, n^2 + 2 is even. Proof: n^2 + n = n(n+1) Since n and n + 1 and two consecutive integers, one must be even and one must be odd so there product must...

1. The angles at the base of a triangle are 35° and 65° respectively. If the vertical angle is bisected, calculate the angles that the bisector makes with the base. First of all, I don't know what is a veritcal angle but I assumed it was the other angle in the triangle. In that case, it was...

For homework, we were asked to prove that \cos^2 \theta + \sin^2 \theta = 1 is true for all angles \theta . Can someone please take a look at these and let me know if they are acceptable. I'm pretty sure the second one works, but I'm not sure of the first one, mainly because the premise of...

i need help for these 2 trig proofs, i did everything i could but it's impossible. 1st question; (cot^2X)-1=csc^2X and 2nd question; (cot^2X)-(cos^2X)=cos^2Xcot^2X caution, both might be insoluable thanks!

everything i have to prove seems impossible then i see it done and it seems so easy any help on starting a proof,...anybody ever have this problem i am new to this stuff, but my problem is I don't know what i need to show and what is legal to use so this is my current problem, I'm sure it's...

It's always annoying when one finds in books (written by (theoretical) physicists for (theoretical) physics students) statements like those below without a mere cross-reference for a mathematically-rigurous proof. And that's what I'm searching for right now: either point me to some books, or...