Bignose

I think that the question of whether physical law has changed is basically unanswerable. We've been studying physical laws for what may be generously called 5,000 years. I would say that serious study hasn't been until the last 500 or so. If something like the gravitational constant isn't so constant but changes 1 ppm per millennium, we aren't going to find that out for a very long time, but such a change can obviously have an effect over billions of years. I think that assuming that what we call constants today are constants is the best assumption for the moment, but I don't think it is outside of the realm of possibility that the "constants" aren't exactly constant. Quite simply, we have only been studying for a very, very, very short time of the Universe.

I think you need to provide more detail. You have B(m,n) and then you have variables x, y, z, and r? I'm confused...

Ooooooooooooooooooo, if it's in red, then it must be bad. I am well conditioned to know that red is bad. Very very bad. Seriously, though. I don't open strange websites or attachments of unknown members. There is just too much risk (and no, no amount of assurance that it doesn't contain a virus is going to change my mind). So, why don't you actually post some of your discussion instead of just telling us to look at your attachment?

Genetic Algorithms as a broad technique, take a set of solutions, keep the ones that are the fittest, remove the ones that are least fit and use the fittest to "breed" new solutions. And repeat. The details are going to highly depend on exactly what you are doing -- as D H said it is an extremely open ended question, so there isn't much more that can be said.

Calculate what matrix? Or what calculations do you want to do with a matrix? Because any programming language that can do loops can be used to do matrix calculations, obviously some better than others. There are many matrix-specific routines out there, depending on whether you are inverting a matrix, or decomposing it, or finding the eigenvalues, etc. etc. And, then, usually depending on what type of matrix it is -- like symmetric, antisymmetric, sparse, Hermitian, etc. -- there are special routines that take advantage of the special type. And, finally, the correct tool really depends on the application. If you just have a single 6x6 matrix you want to invert, even Excel 2003 can do it. Matlab is a good more general tool, but there are other math programs that may be better for what you want to do, too, like Mathematica or Mathcad. Lastly, for most complex situations, writing your own code in Fortran or C is usually best. You can then write your own matrix manipulations or use canned subroutines in a mathematical package of some sort. All-in-all, to get better recommendations I think you need to provide a lot more detail about your application.

Just to make sure, you aren't using auto-recalculate right? Because you should be able to make plenty of changes every time without enduring the several minutes of re-calculation time. Also, if your sheet is that big, I do wonder if Excel is really the best tool. If you are calculating a lot of things, writing a program in Fortran or C or even using a dedicated math language like Matlab may be better. If you are manipulating a lot of data, Access or some other database may be better. But, to answer your question, it is RAM and processor speed that will make the biggest difference. And, if the two options are more RAM and slightly slower speed or more processor speed and less RAM, I'd take more RAM every time.

You certainly do have that in your proof. You start with the assumption that [math]y \ne z [/math] and yet using the axioms you find that [math]y=z[/math], seems pretty contradictory to me. Your proof is virtually identical to mine. You just used y's and z's instead of [math]0_1[/math] and [math]0_2[/math]. A change in nomenclature is just an aesthetic difference, nothing more nothing less. In my proof, I started with assuming that [math]0_1 \ne 0_2 [/math] and using the same axioms found that [math]0_1 = 0_2 [/math]. Seems pretty contradictory to me. So what again is the issue?

The link Sama posted is good. If you don't mind doing some long division, I always liked the divide and average method. I.e. say you were trying to find the square root of 10, and you just guessed that it was 3. Now, divide 10 by 3 and you are left with 3.333333. Average the two results and you get 3.166667. Now, use that average as your next guess. Divide 10 by 3.16667 and you get 3.1578. Average the two again and repeat. This will converge to the square root (3.1622). It isn't fun to do it all by hand, but it can be done. How much work it is depends on how accurate you need the result to be.

I'm a little confused at this statement -- you don't need a calculator to use the quadratic equation, you just need the formula. The solutions of [math]ax^2 + bx + c = 0[/math] are: [math]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/math] There is no need for a calculator, this is the solution. To show that, you should plug that into the equation and actually see for yourself that the expression becomes zero. You don't need a calculator to the algebraic manipulations.

I gave you the reference (and two different ways to get a hold the book) above. The proof above is good enough for Shilov, one of the most renowned Russian mathematicians (this is a man who has published works with Kolomogorov and Gelfand, also very famous Russian mathematicians). If it is good enough for Shilov, it is good enough for me. Considering that at the top of this thread you didn't even know what a proof by contradiction is, why are you being to belligerent that the proofs you have been given aren't proofs by contradiction? These two are quick and easy examples. The examples can get much more complicated, but what I don't understand is why you keep arguing about what a proof by contradiction is? Why can't you accept that these are indeed proofs by contradiction?!?

Maybe it is a language issue; whatever it is, I'm done helping. I've done quite, quite enough. I've always had proofs of this kind referred to as "proofs by contradiction". Maybe you are taking that to mean something else, I don't know. I gave you hints, then I gave you a reference to look it up yourself, then I even provided the proof. There is no more help to give. And, maybe it is still a language issue, but almost all your posts directed to me have seemed very rude, so don't expect much more help from me in the future, either.

The book is available from Amazon, http://www.amazon.com/Elementary-Complex-Analysis-Dover-Mathematics/dp/0486689220/ref=sr_1_1?ie=UTF8&s=books&qid=1246730105&sr=8-1 and any good library (university or city) will have an inter-library loan desk where you can request almost anything. My local city asks only a nominal fee to cover the cost of inter-library loan ($1). $1 to get any book available anywhere is truly amazing. ---------- And, as posted above, the two proofs you have are proofs by contradiction. Since it is already posted on the other forum, there's no point to not copy it here, too. So, assume that there is NOT a unique zero, but they both obey the rules for a zero. Denote them [math]0_1[/math] and [math]0_2[/math]. They both obey the rules of a zero so: by the axioms: for any a: [math]a+0_1 = a[/math] and [math]a+0_2 =a [/math] So, start with [math]0_1[/math] Now [math]0_1 = 0_1 + 0_2[/math] because we can add a zero to it without changing it by the axiom. Now, we can change the order of addition by another of the axioms, so [math]0_1 + 0_2 = 0_2 + 0_1[/math] Now, we manipulate that RHS again by the axiom involving the zero. [math]0_2 + 0_1 = 0_2[/math] Putting it all together: [math]0_1 = 0_1 + 0_2 = 0_2 + 0_1 = 0_2 [/math] or taking out the middle stuff since they are all equal [math]0_1 = 0_2 [/math] The statement [math]0_1 = 0_2 [/math] CONTRADICTS the assumption that we made when we started, namely that [math]0_1[/math] and [math]0_2[/math] were not the same, because we derived that they are in fact equal and therefore the same. Therefore, the opposite of the assumption is true; specifically it is false to say that there is not a unique zero; or removing the double negative, that there is a unique zero. Proof by contradiction.

Nice. The rule on the forum about not spoon feeding work to other people has been mentioned several times, and yet you insist on demanding it. I even found the book that I know a proof exists in, have you even looked in the book I cited? I mean, for goodness sakes, the proof is even on the first 10 or 15 pages or so, you don't even have to read the whole thing! Learning how to look things up for yourself is a valuable skill, too. Not everything is going to be able to be gotten from members on a forum. Edited: I guess you did find someone to spoon-feed you your answer, congratulations: http://www.mathhelpforum.com/math-help/discrete-mathematics-set-theory-logic/94153-proof-contradiction.html So, since you already had that in hand, why the need to come back and complain?!? Funny, funny, stuff.

The other trick is to raise everything to the exact same power and then equate powers. i.e. [math]\frac{1}{2} = 8^c[/math]. Figure out what power 8 needs to be raised to to equal one half and then equate what is in the exponent on the LHS to what is in the exponent in the RHS. Both methods give the same answer, and actually both methods use the same idea (you will use a logarithm to find what power to raise 8 to to equal 1/2 whether you knowingly do it or not). That said, I think that the logarithms route is the better one to know, because logarithms have several useful relations that typically make these problems easier.

I am not going to give you the proof, one more time I am not going to do your work for you. However, I know for a fact that a proof by contradiction is given in Shilov's Elementary Real and Complex Analysis.

I can play this game, too: All you have been told are facts, yet you refuse to know. Regards. ----------- Dang... if only there was a way to solve this impasse.... Hmmmm, what if... no... no wait ..... wait.... wait... what if each side brought some pieces of evidence to the table and we all decided which tasted better... no, wait, not tasted better, how about which evidence smelled better. Yep. Smelled. ... ... No, wait, I have an even better idea! Maybe let's use the evidence to decide which hypothesis is fit better. Yes, that's it. Let's all bring all the available evidence together and see which model it fits better. ----------- If that doesn't fire up the ol' neurons, here's another example. What you are doing right now is analogous to giving testimony in a courtroom. You are trying to convince a jury that what you believe you saw is the truth. A good witness answers every question asked by the lawyers as accurately as possible. You are answering every question with "Mr. Smith did it." Lawyer: "What was the weather like that day?" You: "Mr. Smith did it." Lawyer: "How far away were you when you first saw Mr. Smith?" You: "Mr. Smith did it." Lawyer: "Had you ever met Mr. Smith before that day?" You: "Mr. Smith did it." Lawyer: "What clothes was the assailant wearing that day?" You: "Mr. Smith did it." Lawyer: "What time was it?" You: "Mr. Smith did it." Lawyer: "What street were you on?" You: "Mr. Smith did it." Do you see how such a witness would probably be completely dismissed by jurors? A good witness answers the questions asked, and doesn't just repeat over and over and over. That's all we're asking of you, to answer all the various questions. Repeating over and over and over and over is worthless and completely unconvincing. Convince us by being a good witness.

Why is your repeat and repeat better than the other members' repeat and repeat?!? Why don't you take your own advice here and open your mind and actually critically evaluate evidence as to which idea is better?

But there isn't equilibrium of mass. The mass of a proton is 1836 times the mass of an electron. But, why let a little things like facts get in the way of a good story?

A gradient in pressure. A gradient in surface tension. Gravity or any other body force (i.e. the forces a fluid feels in a centrifuge). Or it may even be as simple as a moving boundary drives fluid flow. A gradient in density is only one of many reasons fluid may flow. Note that my statements were about fluid dynamics, which you included in your statement "This is also relevant to aerodynamics/hydrodynamics/field theory etc... ", which just isn't right. I don't know electricity and magnetism nearly as well as fluid mechanics, so hopefully someone else can come along and answer your question.

Then that sounds right. It wasn't very clear what the situation was -- I was thinking of a fixed list that gets rearranged, but doesn't re-sample with replacement. All of these conditions (and how to use the mathematical terminology to explain it better) should be covered by such a class.

No, you aren't using the conditions right. Going with 20 again. To start, assuming a uniform distribution, it is indeed a 1 in 20 chance that the 1st video is the oldest. But, now you need to use that condition that the 1st video is already the oldest. That leaves 19 more to be distributed uniformly again. So, the chance that the second video is the second oldest is now 1 in 19. And so on. You end up with 1 in 20! chance, not 20^20.

Same thing in hydrodynamics. A gradient in density does cause a fluid flow, but isn't the only reason for a fluid flow. There is an entire branch of hydrodynamics wherein the density is assumed to be a constant, and yet there is plenty of interesting flows to study.

Limits can be introduced into pre-calc, too. Basically it is a brush-up to make sure your algebra and trig skills are good enough for calc. If you were a good student in algebra and trig, you probably should not need pre-calc.

It is a problem based on conditional probabilities. First, you calculate the odds that the 1st video in the playlist is the earliest chronologically (assuming some distribution of the random variables, probably uniform). Then, with the condition that the 1st video is the earliest, what is the probability that the 2nd video in the playlist is 2nd earliest. Then with the condition of both the 1st and the 2nd video are in the right order, what is the probability that the 3rd is also in order, etc. etc. If you know how to calculate those probabilities -- this is probably one of the many topics the class will cover -- it isn't hard. A lot of times the trickiest part of a probability question is to make sure you are answering the question as asked. The recent raffle thread in the other math sub-forum is a good example. I didn't read the question exactly right and wasn't answering it exactly right.

I am a little confused. Is this a homework problem? Are you supposed to know it before you went in? Or is it something that you are going to learn how to do? Because if this is a class on probability, then these are the kind of problems you will learn how to answer. Whether it is "hard" or not is going to depend on how well you learn the material (which will be a combination of your study habits and will to learn and some natural ability, too). One problem isn't a good indicator of how hard a class it will be. What does the syllabus look like? How about the text? How about the impressions other people who have taken the class have?