Proofs Definition and 699 Threads

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...

A jet of liquid of cross-sectional area A and density p moves with speed vj in the positive x-direction and impinges against a perfectly smooth blade B, which deflects the stream at right angles but does not slow it down. (a) If the blade is stationary, prove that the rate of arrival of mass at...

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...

Hi. We are doing permutations and combinations in class and we were given some formulas without proof to remember. I was able to derive most of them but was unable to derive 3 of them. But I would like to see how do I derive them for sake of fun (also if I forget them what will I do. :) ). 1...

Short question: Can anyone provide me with a nice synopsis of how to go about proving the "existence" of some object as often requested in math questions such as, "prove that X really exists and is unique"? In other owrds, in general, when presented with an "existence" question, is there a nice...

Can anyone please help me with this proof Prove that every positive integer, ending in 5 creates a number that when squared ends in 25

I'm not sure if I should've started a new thread for this but.. I need some help trying to prove that the diagonals of a parallelogram bisect each other.. I think I have an idea of how to solve this but I can't seem to put it together: Given AB = DC AD = BC Known AB + BC = AC BC + BD = BD...

Vector Proofs: A Quadrilateral thing #2! Thanks lightgrav!

Just a couple questions that I'd appreciate any help on. 1. if [(2^d) - 1] is prime, prove that d is prime as well. 2. Prove that (p-1)C(k) is congruent to (-1)^k mod p. I've started them both but ended up getting stuck. Any ideas? Thanks

I am currently having a lot of troublw with delta-epsilon proofs--can someone please help explain how they work and how to do them Thanks

Hello everyone, I have a little website dedicated to helping people learn math, write proofs, and learn physics. I have a list of books to help people learn math and physics, links to free online books, and online courses. Please vist my website and if you have any questions feel free to email...

This year I'm a freshman at university - physics - and we are just starting with mathematical analysis. I don't find it that difficult, but my problem are proofs. They are not hard, but I sometimes can't prove even the easiest things (I know why it is so, but can't put it down on the paper). Can...

I really really hate proofs! I've done 3 of my 5 problems, which took me 2 days and over 30-50 pieces of scrap paper. I'm serious, I didn't even eat dinner today because I spent straight hours just staring at questions, thinking I was coming close to solutions, then only to find out I've...

Hi all, If I have these two statements given to me, and I have to determine whether they are true or not. a) \forall x \epsilon R \exists y \epsilon R (y^2 = x^2 + 1) b) \exists y \epsilon R \forall x \epsilon R (y^2 = x^2 + 1) Now, to me, they both mean exactly the same thing...

I have a set theory that I want to prove is consistent if ZFC is consistent. I'm dimly aware of what to do or where to begin. To keep the notation straight, A[0] is the set of axioms in ZFC. A[1] is the set of axioms in ZFA, antifoundation. I know that A[0] consistent implies A[1]...

Help on proofs? pleasee Hi there, I was given these proofs to do for my quantum class. proofs are the worst for me, I know it work and i have and idea how it starts which i wrote in the image but I can't seem to figure out the inbetweens. I've attach the images, if anyone can help me that...

Hi, right now I am struggeling with this (calc1). To be honest, I nearly don't understand a thing. What's going on, and when am I done with the proof? I can plug in the limits and the approached value into the formal definiton of a limit, but that's as far as I get. (I semi-get the easy...

Can anyone help me start this out? I got absolutely no clue. Q: If A and B are n x n matrices, AB = -BA, and n is odd, show that either A or B has no inverse. I know that we have to show that either det A is 0 or det B is 0, but I have no clue how to show it with the given information...

can anyone help me with the proofs: 1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots=\frac{\pi^2}{6} if F_i is the ith Fibonacci number, then F_1+F_2+F_3+\ldots+F_n=F_{n+2}-1 F_2+F_4+F_6+\ldots+F_{2n}=F_{2n+1}-1 F_1+F_3+F_5+\ldots+F_{2n-1}=F_{2n}...

T* is a recursive definition, a subset of the family of ternary strings. Let T* be the smallest set such that: BASIS: 0 is in T* INDUCTION STEP: If x,y in T*, then so are x0y, 1x2 and 2 x1. a) Prove that if k in N, then there is no string in T* with exactly 3^k +1 zeros. b) Prove that if...

Are there any sites that have most of the popular geometry proofs? Thanks.

I want to be a physicist when I'm out of college, but I see a humongous obstacle in proofs. See, I had taken Calc III and Diff Eq earlier this year, and aced them, but when I got to linear algebra, my first proof-based course, my grade dropped to a C+. (I have my final tomorrow, btw, and I'm...

I am "scared" (to put it mildly) of these problems, which I need to review before my final tomorrow. Just to let all of you know, this is not homework. There are 25 or so problems, and I only understand around 10 of them. :frown: Help me! I need an A on the final to get a B in the class. :cry...

After seeing infinite sets defined negatively, I liked seeing them defined as sets that are equivalent to one of their proper subsets. I always thought diagonal argument[/url] was cool. Do you have a favorite definition, theorem, proof, bit of knowledge you found especially insightful or...

Hi, I am having trouble with these proofs; I don't know if I am doing these right. I'd appreciate some help. Thank you. If X---> y is a map, then let B1, B2, B \subseteq X. i. f(B1 U B2) = f(B1) U f(B2) To prove this I have: f(B1 U B2)=f(B1) U f(B2) Since B1 U B2 \subseteq B1, we...

Linear Algebra proof I would appreciate any help with any of the foolowing: 1. Let C be a countable set. Prove that any linear well-ordered on C with the property that whatever c in C there are only finitely elements c` with c`<c, is unduced from the canonical order on N via a bijection N->...

I need help solving these 2 proofs: (sec^2x-1)/(sec^2x) = sin^2x I am not sure what direction to go in. I know the top of the left side could be changed into: tan^2x/sec^2x, but I don't know what to do after that. The second one I need help with is: cos^2x/(1+tan^2x) = cot^2x I...

I need help solving 2 proofs: tan x + cot x = (sec x)(csc x) I changed the left side to: tan x + 1/tan x = (sec x)(csc x) then crossed out the tan: 1 = (sec x)(csc x), but I got stuck there. The next one I had trouble with was: tan^2 x - sin^2 x = (tan^2 x)(sin^2 x) I saw...