Proofs Definition and 699 Threads

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...

Hi, I have a major test next week and some questions will be on epsilon and delta proofs. From the homework I have done, these epsilon and delta proofs can be applied anywhere and in any scenario. Therefore, I was wondering do you guys have any tips on handling and solving these questions...

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...

Where can I find some good problems involving finding proofs? I want to see how far I can go as it's relatively new to me...

Hey I have 2 quick questions... 1) Any advice for proofs, I am just starting with them, and wondering how I can make good proofs, i know very little about the now :| anything that other people expierienced while starting proofs would be great, (its grade 12 algebra) 2) Anyone know where...

Let f:X->Y be a function 1) Given any subset B of Y, prove that f(f^-1(B)) is a subset of B 2) Prove that f(f^-1(B))=B for all subsets B of Y if and only if f is surjective Help anybody?

Hello everyone, I'm a budding theoretical physicist and mathematician, all throughout my education I've been taught about mathematical objects, relation between objects, Proofs, etc. Never have I been taught HOW to actually learn math. I've put together a website with all the lessons on how...

Ok, I've seen many proofs of this, all being the same, but the closest I could find online was here: http://freespace.virgin.net/mark.davidson3/IMS2121/buoyancy/Buoyancy.html Basically the idea is you mess around with the formulas for pressure and hey bingo. However, I have one question - the...

Thanks in advance for any help, I'm trying to understand epsilon-delta proofs, and the various sites I've found so far aren't helping that well. I know that epsilon is referring to a small number >0, and delta traditionally refers to a number > epsilon, but I'm not quite sure of why this...

How do I show |Rez - Rez0|<E whenever 0<|z-z0|<D is true, where E and D are real number greater than 0, and z is obviously a complex number? In other words, proving that the lim of Rez (as z approaches z0)=Rez0.

Im looking for some proofs on the rationality of pi. I also want to know what some people think about it.

Know any 'nice' proofs in maths? Or know an alternative and simpler/nicer proof to common method employed? Post here ==>

I'm sure most of you already know this. The real point of the thread is finding different ways of approaching it. You see, I have a friend who refuses to accept what seems to me to be so obvious: .9 repeating (infinite 9s after the decimal) is exactly equal to the whole number 1. Here are the...

Do mathematical proofs exist, of things that we are not sure exist, especially those, that do not have observational confirmed data?

I know this is below most of those that peruse these forums, but I've been giving myself an ulcer trying to figure these silly things out. The first problem starts out as (1-sin^2(x))(1+tan^2(x))=1 and I've got it down to (sin^2(x)/tan^2(x))-sin^2(x)=1 but from there I've got no idea...

Ok, I know about the search for supersymmetric partner particles (sparticles) and the tests on gravity variance at small scales, but what other tests are there that can be used to add proof to superstring theory?

I understand how to use such things as product rules, quotient rules, parts by integration, but it bothers me I don't really have a deeper understanding of it. My book offers rather rigorous proofs, they are all pretty much: assume this to be this and let this be that so it must equal this...

I'm having trouble with two parallelogram proofs 1) PQRS is a parallelogram and T is any point inside the parallelogram. Prove that triangle TSR + triangle TQP = 1/2 parallelogram PQRS 2) ABCD is a quadrilateral whose area is bisected by the diagonal AC. Prove that BD is bisected by AC...

Hello, First I will post the question that I am working on. I am not good at proofs (even elementry proofs such as these ones). I was wondering if someone could take a look at my work and perhaps confirm whether my proofs are adequate and/or make some suggestions. First I will start...

I was having some serius problems when proving some of the questions where we are given, let's say, a rectangle, there is one diagnol, and the other diagonal is connected to a line that is in a ratio, and the diagnal connects to the point that divides that line. The concept is combined with...

[SOLVED] Geometry Proofs. Hello, I am currently taking a second year mathematics course in geometry at university. I have to do quite a few proofs and I am not used to doing proofs much less geometry proofs -last time I took geometry was when I was in grade 10 and that was over ten years...

Hi! I'm new to the forums. I'm taking an introduction to physics class this semester and I've been having some difficulty with it. Oh, I also wanted to let you know that it's been a while since I've taken calculus or any other math class for that matter. But I need physics to graduate. Anywho...

Hello everyone, My first post on these forums and I was wondering if I could have some assistance/direction with a problem: Prove that if p is a prime number and a and b are any positive integers strictly less than p then a x b is not divisible by p. The first thing I thought to myself...

Backward induction Is there any proof that involve the use of back induction besides the proof of AM>=GM ? It is the only example I've come across that use back induction.