Recent content by privyet

Thanks for your reply. 1) I'm not sure, to be honest. One approach I had in mind was to say let x = y, then in the assymetric relation xRx \Rightarrow \neg(xRx), then using the irreflexive relation I can say that since xRx is the premise it is false and therefore the implication is vacuously...

Homework Statement Prove the following properties of relations: 1) If R is asymmetric then it's antisymmetric. 2) If R is asymmetric then it's irreflexive. 3) If R is irreflexive and transitive then it's asymmetric. The Attempt at a Solution 1) If R is asymmetric on a set X, then for all...

Thanks again for the help. Factoring by decomposition will be a big help.

This topic is definitely not as simple as good rebels vs bad Assad. Here's an article that suggests that the rebels were behind the massacre in Houla: http://www.atimes.com/atimes/Middle_East/NG24Ak02.html

Thanks LastOneStanding, another rookie mistake on my part. I have to admit that I cheated with the factorisation (thanks WolframAlpha). I don't know if there's a specific method I should follow to factorize something like 4(r−r2)−1, but I still find it very difficult to just guess at what the...

Thank you all for the advice. First of all, I did mean 1/(r(1−r))≥4. The exercise comes from the 4th chapter of the book, which focuses on applying direct proof and contrapositive proof methods to basic proofs of integers, real numbers and sets. So I guess the approach suggested by...

Homework Statement This is an exercise from the book 'Mathematical Proofs: A transition to advanced mathematics'. Prove that if r is in ℝ and 0<r<1, then 1/r(1-r)≥4 The Attempt at a Solution My guess is that it would be best to use a proof by contrapositive. So I start by assuming...

Great! Thank you both for your help.

I was saying that I could see that it looks pretty obvious that if n divides a-b, it will divide a2-b2, but that I didn't know how to prove it. Using oay's hint about factorisation I've got a2-b2=(a+b)(a-b) and since n divides a-b, n therefore divides a2-b2 but this is looking very different...

Yeah. I know its simple but I just don't know how to think about it.

Homework Statement This is a question from the book I'm studying called 'Mathematical Proofs: A transition to advanced mathematics' Homework Equations Let a, b, n be integers, with n≥2. Prove that if a\equivb(mod n), then a2\equivb2(mod n). The Attempt at a Solution Following the examples...

What kind of information are you looking for? Academic papers or just news articles from the time? Obviously academic stuff will be a lot harder to come by. A few sites that might help you are: http://www.crikey.com.au/topic/election-2007/ (Australia's best independent news site)...

Thank you both. I'm afraid that I wasn't able to get to far using just the definition. Not really having any experience with proofs it is difficult to know what is sufficient, it seems that sometimes something ostensibly very simple or obvious has quite a complicated proof, so it's good to see...

Homework Statement Continuing with my Apostol efforts. From Section I 2.5: These exercises go over some of the absolute basics of sets. In 3. I'm given A = {1}, B = {1,2} and asked to decide whether some statements are true or false, proving the ones that are true. Seeing which ones are...

Homework Statement derive a reduction formula for ∫(lnx)n dx and use it to evaluate ∫1e (lnx)3dx Homework Equations The Attempt at a Solution In other examples we've started by saying ∫(lnx)ndx = ∫(lnx)(lnx)n-1dx and using integration by parts. So let: f = (lnx)n-1 f' =...