Proofs Definition and 671 Threads

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!

[FONT="Century Gothic"]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

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 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...

hello everyone. i was once a math major until i got a bit taste of what upper div math is like. proofs! can't say that i like it at all. i guess I am the type of guys who can't do proofs whatsoever. currently taking linear algebra, struggling a bit. so sometime ago, i changed my major to...

I find proofs very difficult. What process would you go through before writing a proof? What do you do generally?

I'm taking a first course in modern physics and were currently discussing special relativity. My professor keeps using four-vectors in derivations and proofs, and requires us to use them, but he hasn't developed the theory behind them; that is he's only showed us how to manipulate them. The...

I recently posted about some trig equations, now I'm doing some HW on trig proofs, i got the first couple trig proofs, but had trouble with the last two. Here are the two problems (attached). For the first one, i can't even get started. i have some ideas, but i can't find out how to get the...

Constructing Proofs help! Here is the problem: Given a set S and subset A, the characteristic function of A, denoted \chi_A, is the function defined from S to \mathbb{Z} with the property that for all u \ \epsilon \ S: \chi_A(u)= \begin{cases} 1 & \text{if u $ \epsilon \ A$} \\ 0...

Hey guys… and girls! I was just wondering if anyone knew of any good books that introduce the concepts and reasoning behind mathematical proofs, starting from the beginners level. (In high school my teachers did not emphasize proofs.) I would like this specifically to help me for first year...

I have to teach the "bridge" course for junior level math and math ed majors on proofs and logic, and need to find a book. I do not like books that are mathematically vacuous. I.e. I want one that teaches how to prove things and then actually proves something of mathematical interest...

I'm trying to prove the following by contradiction: [(A^B)-(B^C)]-(A^C)'=0. A, B, C are sets. All I know is in order to prove by contradiction you simply set the above not equal to zero. But I don't know where to go from there. "^" means the intersection symbol.

Definitions: Briefly, for the formal, object language L, there are two mutually exclusive categories of primitive symbols: (i) an infinite set of propositional symbols and (ii) two distinct connectives, ~ (negation) and -> (implication). If s_1, s_2, ..., s_l are (not necessarily distinct)...

community college and the lack of teaching proofs I'm in calculus II and to this date i have never had to write one proof! when i look through the forums i commonly come across postings about how to prove things, even from high school kids. why are community colleges less rigorous than 4 year...

need some urgent help with basic complex analysis (no proofs) This forum is probably more appropriate. please forgive me for double posting. Can someone give me examples of the following? (no proofs needed) (C is the complex set) 1. a non-zero complex number z such that Arg(z^2) is NOT...

need some urgent help with basic complex variables (no proofs) Hi: can someone give me examples of the following? (no proofs needed) 1. a non-zero complex number z such that Arg(z^2) "not equal to" 2 Arg z 2. a region in C which is not a domain 3. a non-empty subset of C which has no...

I plan on going onto grad school at some point in the near future and I know I could use a ton of work in the area of constructing proofs. What I'm looking for is a book that could shed some light on how this process is approached. That is to say for example maybe how a mathematician would...

i just started my second semester with geomtry and am having difficulties with these proofs. i am stuck on this one question which asks: prove that if n is an odd positive integer, then one of the numbers n+5 or n+7 is dividsible by 4. so this is what i came up with: let n = 2k+1...

I'm confronted with the following question that may of may not have a solution: You are given eight variables, A, B, C, D, E, F, G, and H. These variables are integers. You know that: A/B > E/F and C/D > G/H Is it possible that (A+C)/(B+D) < (E+G)/(F+H)? I've tried...

Hey, anyone ever done indirect proofs? Maybe my school is a little weird, but we are doing those. IF you did, how do we shape the proof?

I'm looking for a book that gives you many equations and goes through proofs etc. One of my weaknesses mathematically tends to be logically getting from one point to another when I'm not solving problems numerically and remembering what are and what are not legal steps to prove something. I'm...

I am teaching honors calculus in college, and trying to teach something about convergence of sequences and series. my class has apparently never seen a genuine proof in high school and have no idea how to begin one (answer: with the definition). I have had students ask me what "QED" stands...

Fundamental mathematic proofs... I know this may seem a slightly odd question, but are there any website or pdf files, etc, floating around of proofs of the basic pricipals and "tricks" of maths? eg - adding, subtraction, multiplication, division, fractional sums and products, percentages, etc...

heres a little problem that at a first glance is real: \frac{1}{-1} = \frac{-1}{1} so \sqrt{\frac{1}{-1}} = \sqrt{\frac{-1}{1}} by splitting it the square root into two parts... \frac{i}{1} = \frac{1}{i} and i^2 = 1 -1 = 1 wonder if there are any more similar "proofs"?

I'm tutoring a girl in my math class on how to write proofs. She understands what information she needs to prove something, but the only problem is she doesn't understand how to put the data in order. I tried to the following to clear things up for her: 1.) I asked her to prove...

I am in grade 12 physics, and i have to practice equation proofs. I am currently studying work, kinetic energy, springs, and potential energy (gravity and elastic). Does anyone have a good proof?

Proofs of a God or no God are pretty much useless? I sometimes find myself staring at the absurdity of looking for a proof for the existence of a God, or the proof for the non-existence of one. My logic is pretty simple, say if we say that a orderly universe implies existence of a God, but...

I was just wondering, since i m kind of weak in doing proofs, what is the best way of understanding on how to do proofs. What is the best way to master, if one can, on doing proofs? or even if not master, but to be able to do proofs without "thinking", like sometimes my teacher says he just does...

Guys, I'm trying to prove by induction that the sequence given by a_{n+1}=3-\frac{1}{a_n} \qquad a_1=1 is increasing and a_n < 3 \qquad \forall n . Is the following correct? Thank you. :smile: Task #1. n = 1 \Longrightarrow a_2=2>a_1 is true. We assume n = k is true. Then...

We didn't talk about prime numbers in my class, but several of the homework problems mention them. For instance: Prove that if every even natural number greater than 2 is the sum of two primes, then every odd natural number greater than 5 is the sume of three primes. Assume that n is an...

Here's my problem: Provide either a proof or a counterexample for each of these statements. a) For all real numbers x and y, if x is greater than 1 and y is greater than zero, then y^x is greater than x. My proof: Suppose x is some real number greater than 1 and y is some real number...