Sam Jones
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 Nov 8 comment Deciding If A Relation On A Set Is An Equivalence Relation For it to be transitive it has to satisfy $aRb \wedge bRc \Rightarrow aRc$ for ALL $a, b, c$ in the set that the relation $R$ is defined on. See if you can find one example where this isn't satisfied. Nov 6 comment Understanding simplification of an algebra problem $x^3 - 2x^2 = x^3(1 - \frac{2}{x})$ if you multiply the right hand side out you will end up with the left hand side. Oct 19 comment Successive Bounces of Ball Paradox I think we'd need to figure out what assumptions we would be using, we obviously wouldn't be modelling real life if we allow the height of each bounce to be fixed so what are we doing, what assumptions do we have and what reasoning is valid. What axioms are we using? It's possible that those two assumptions (constant horizontal velocity and constant height for each bounce) would lead to a contradiction and that no meaningful answer could be obtained, if this were the case then it wouldn't be possible to resolve the paradox as in an inconsistent system every statement is true (or provable). Oct 18 comment Successive Bounces of Ball Paradox You could add the assumption that the height of each bounce is constant and it is only the frequency of each bounce which increases. I'm not sure what could be said about the ball's position after 2 seconds in that case, I'm not even sure that the question would make sense. I think the main point to this question and answer is that you have to think about what assumptions or restrictions you're putting on the problem and this problem appears difficult because not all the assumptions have been stated. Oct 18 comment Successive Bounces of Ball Paradox I think the problem is that the ball can't keep moving in the air beyond 2 seconds. Assume the velocity is 1m/s. After 1 second it has travelled 1m. Now the next bounce takes 0.5 seconds and it travels a further 0.5m, right? So after 2 seconds it has travelled 2m. But now the bounces are so small that it's rolling. Yes, the horizontal speed is still 1m/s but it's no longer covering that distance whilst in the air. So the total horizontal distance covered whilst in the air is 2m. Oct 18 comment Successive Bounces of Ball Paradox But, you believe (I assume, because you stated it) that the sum of the geometric series is finite. So you must believe that an infinite sum of finite numbers can be finite. So why do you think that method 2 is in any way correct? If I've understood your argument correctly then you are saying "An infinite sum of finite numbers must be infinite." Oct 18 comment Successive Bounces of Ball Paradox To start with, you only want to count the horizontal distance covered whilst the ball is in the air (you haven't explicitly said that, though). Secondly, the horizontal distance covered whilst the ball is in the air is bounded above by 2m and you can get arbitrarily close to this by measuring the distance covered over a longer time. This is just a rewording of this: en.wikipedia.org/wiki/Zeno%27s_paradoxes Aug 15 comment What is a cyclic integral? I had never heard of cyclic integrals either, so I used google and came up with this: sciforums.com/… Jul 31 comment Does “nullity” have a potentially conflicting or confusing usage? Who ever said mathematics had to be fair? :P Jul 3 comment Last few digits of $n^{n^{n^{\cdot^{\cdot^{\cdot^n}}}}}$ Whilst this is true, I think the usual convention is that the brackets start from the top. So $x^{y^z}$ becomes $x^{(y^z)}$ Jun 25 comment Must a function that 'preserves r.e.-ness' be computable itself? This is a very nice answer, do you have a reference for the result about the existence of cohesive sets? May 21 comment Problems about symmetric groups And this video: youtube.com/watch?v=8M4dUj7vZJc explains the episode and the proof very well. May 11 comment Issues with text problems I think this question is extremely difficult to answer. Personally, I don't believe that there is a "one size fits all" approach to problem solving which will work for everyone. Your general method of: (1)what do I have? (2)what do I want? (3)how do I turn what I have into what I want? Is as good as one can do, in general (in my opinion). The problem in this particular question seems to be that the student is unsure of what the question is actually asking them to calculate. May 10 comment Trig limit of $\lim\limits_{x\to 0}\frac{\sin{6x}}{\sin{2x}}$ No problem, this site uses some form of latex for displaying equations, you have to surround the mathematics with \$for an inline piece of mathematics and \$\\$ for a "displayed" piece. en.wikipedia.org/wiki/LaTeX might be a good place to find out more. Apr 28 comment is it possible to get the Riemann zeros I'm not entirely sure what you are asking but it seems to be related to what I'm about to say. It is entirely possible to calculate actual zeros of the Riemann-zeta function (up to some given height in the complex plane) and verify that they all(up to that height) lie on the critical line. This has been studied extensively, notably, by Odlyzko: dtc.umn.edu/~odlyzko All the information you would need to implement some algorithms and do some calculations yourself are in this well known and cheap book: amazon.com/Riemanns-Zeta-Function-Harold-Edwards/dp/0486417409 Apr 24 comment Subgroups in Group Theory? As mentioned by Alastair Litterick, I think you are looking for this: en.wikipedia.org/wiki/Lagrange%27s_theorem_%28group_theory%29 but you should probably try to understand the basic definitions of groups, subgroups and cosets before you try to understand a proof of Lagrange's theorem. Apr 23 comment Logical Equivalance As said by countinghaus, truth tables consider every possible true/false assignment to each variable p, q and r. so you simply draw a table with the value of p, q, and r in it, you can then work out the value for q implies r for each row and then the value for p implies (q implies r) and similarly for the second expression, if the tables are the same then they are equivalent, but you will find that they differ on the row I mentioned. Have a look at en.wikipedia.org/wiki/Truth_table#Logical_implication for more information and an example.