Dapthar

The constitution would have to be amended for a non-natural born citizen to become President. (Source: http://en.wikipedia.org/wiki/President_of_the_United_States, specifically, the "Requirements to hold office" section.)

When applicable, lifestyle changes are effective at treating the root of some chronic conditions. I also advocate taking drugs only when absolutely necessary, otherwise, the medicine may become less effective over time, or worse, in the case of unnecessarily taking antibiotics, one can unknowingly create a drug-resistant strain of a disease. However, holistic treatment is not a viable replacement for modern medicine. Why? As I mentioned before, simple symptoms of a disease can be deadly. For example, consider allergic reactions. Some children have severe allergic reaction to peanuts, and usually, they find out via allergy tests that they undergo when they are very young. However, if one avoids doctors except when an emergency arises, the first time a parent finds out about such an allergy could be when their child experiences an anaphylactic shock. To those not knowledgeable about this condition, it may easily be confused with choking, and by the time one realizes what's happening, the child may already have brain damage due to lack of oxygen, or even worse, the child may die. If a parent is aware of this condition, and their child experiences it, then they could inject them with an EpiPen shot (EpiPens are auto-injectors for epinephrine) and provide their child the necessary time to get to the emergency room. (Source: http://www.epipen.com/epipen_main.aspx) The point is, if you only go to the doctor when you have a problem, then you may not find out about serious medical conditions until it is too late. If I remember correctly, the only "safe" vitamin supplement is vitamin C, since any accidental overdose is passed out through one's urine. However, 'fat soluble' vitamins can be very dangerous to take, since they take longer to be removed from the body, increasing chances of a toxic overdose. (Source: http://www.prn2.usm.my/mainsite/bulletin/sun/1996/sun43.html) Thus, vitamin supplements are far from being "essentially food". While I commend your conscious alterations to diet and dedication to regular exercise' date=' I reiterate that, as in the aforementioned example, sometimes one's first symptoms of an illness are life-threatening medical problems. As such, I cannot advocate, in good conscience, visiting a doctor only when a problem arises. Sometimes one must visit them, and push for certain tests to be administered, to determine potential future health problems, such as allergic reactions, or a predisposition for diabetes. In some cases, such as if one has cystic fibrosis, exclusive use of holistic methods is a gamble people simply cannot afford to take. (Source: http://www.cff.org/about_cf/what_is_cf/) Prior to the advent of drugs that thinned the mucous that accumulates in CF patient's lungs, most were doomed to die in early childhood. However, after the advent of such medicines, the average lifespan of a CF patient has been increased to 30 years. (Source: http://64.233.161.104/search?q=cache:PpwJDJhCgNoJ:www.diagnose-me.com/cond/C133239.html+cystic+fibrosis+average+lifespan&hl=en) Yes, but money is what drives research. Granted there is a rather pronounced dark side, namely, the most heavily funded drugs are those that the drug companies predict most people will buy. As a result, there is very little 'profit' in researching drugs whose target audience is primarily people who cannot pay for them, i.e. HIV/AIDS, or making existing drugs cheaper to help stop the spread of diseases that are common in areas with poor living conditions, i.e. cholera. However, the sad fact is, very few people will do anything that does not directly benefit them unless there is a financial incentive. Unlike software, there is a rather large cost associated with drug research, so there is almost no hope of 'open source medicine', if you'll pardon my colloquialism. Thus, no money equals no research, so it is a necessary evil. Primarily those with the ability to pay benefit, but at least through government programs like Medicaid and Medicare, those in need can still, in theory, get the help they require. Thanks. I hope your lifestyle continues to keep yourself, and your family healthy as well.

It's \neq Example: [math]\neq[/math] Also, I vote that the "Quick LaTex Tutorial Thread" be cleared out, so that it can be a bit more effective reference for forumers. Just keep any "tuorial" posts and the links to LaTeX references from the thread, and remove everything else. For convenience, here's all the references that were in the thread:

Yup.

You're right' date=' it's a waste of time to check, since you have four vectors in [math']\mathbb{R} ^3[/math], thus they must be linearly dependent, since there can't be more than three linearly independent vectors in [math]\mathbb{R} ^3[/math].

Intuitively, as [math]x\to0[/math], [math]sin x \approx x[/math], therefore, the limit should be [math] 0 [/math]. At the moment, I'll just give you a hint. If you combine the two fractions, you get [math]\lim_{x\to0}{\frac{x-sin x}{x sin x}}[/math]. This is an indeterminate form (namely [math]\frac{0}{0}[/math]), so you can apply L'Hopital's rule. You'll need to apply it twice, but you'll end up getting that the limit is [math] 0 [/math]. If you haven't learned L'Hopital's rule yet, mention so in a post, and I'll try to compute the limit without using it.

Here's a nice, free speed test. However, you need Java installed to run it, but there are links to download it on the speed test page. Speed Test Link: http://www.dslreports.com/stest?loc=97'>http://www.dslreports.com/stest?loc=97 Link to Speed Test Main Page: http://www.dslreports.com/stest Just for reference, here's my results from the first test listed above: Your download speed: 2344382 bps, or 2289 kbps. A 286.1 KB/sec transfer rate. Your upload speed: 320688 bps, or 313 kbps.

Just a minor correction, but I think that from this point onwards, you substituted [math]3 dU[/math] into the right hand side, but forgot to include the factor of [math]3[/math] on the left hand side. Otherwise, it looked correct to me.

Sure, seems about right. However, you don't need to simulate every particle all the time. It's similar to the way rendering engines in video games work, namely, they only draw what the player would see. As mentioned in the paper you referenced: A complete simulation would require another universe to run the simulation in, but one that people couldn't tell from reality is plausible, or as the author of the paper puts it:

This is because, as you have written it, you have a [math]dx[/math] in the integral, so you must solve for something to substitute in for [math]dx[/math], namely [math]dx = \frac{1}{2} \cdot du[/math].

Here's a solution, but it spoils all the fun: http://www.cut-the-knot.com/impossible/brothers.shtml

If you are uninsured, yeah, you get charged an arm and a leg. Yup. As mentioned by atinymonkey, it's called traveler's insurance. The price of it depends on your trip duration, and how much coverage you want to purchase. It'll probably end up being around $100.00 - $200.00 USD, which translates to about 77 - 155 Euros, if you take the minimum possible coverage amount. Here's a site where you can compare traveler's insurance rates: http://www.insuremytrip.com/myquote-1000-0-13027-339901.html.

That's a rather sweeping generalization, and while certain activities, smoking in particular, increase one's risk of cancer, there are many types of cancer whose primary cause is not due to "lifestyle choices". For example: (Source: http://www.cancer.org/docroot/NWS/content/NWS_1_1x_Large_Study_Links_Tobacco_To_Stomach_Cancer.asp) The currently, it is believed that one of the main causes of this cancer is atrophic gastritis, where: (Source: http://www.cancer.org/docroot/CRI/content/CRI_2_4_2X_Do_we_know_what_causes_stomach_cancer_40.asp?rnav=cri) In my opinion, this is due to the fact that obesity doesn't tend to cause severe medical problems until much later in one's life, and thus, the only immediate negative effect of eating whatever one wants while they are relatively young is a negative social stigma. Care to elaborate? How do you know that they don't have conditions that show few precursors to serious medical conditions, such as such a high cholesterol, or high blood pressure? What about vaccinations? What if they had a serious medical condition whose symptoms are life threatening, but easily treated with modern medicines, such as asthma? I hope that you aren't asserting that holistic treatment are a substitute for a good diet and regular exercise. Your solution becomes a bit muddied when the symptoms of a disease are fatal.

As fara as I know' date=' there is only one Drake equation, namely: ([i']This is largely copied from http://www.activemind.com/Mysterious/Topics/SETI/drake_equation.html[/i]) [math]N_{civ}=N_{star}\cdot f_p \cdot n_e \cdot f_l \cdot f_i \cdot f_c \cdot f_L[/math] Where: [math]N_{civ}[/math] = The number of intelligent, communicating civilizations there are in our galaxy. [math]N_{star}[/math] = The number of stars in the Milky Way Galaxy. [math]f_p[/math] = The fraction of stars that have planets around them. [math]n_e[/math] = The number of planets per star that are capable of sustaining life. [math]f_l[/math] = The fraction of planets in [math]n_e[/math] where life evolves. [math]f_i[/math] = The fraction of [math]f_l[/math] where intelligent life evolves. [math]f_c[/math] = The fraction of [math]f_i[/math] that communicate. [math]f_L[/math] = Fraction of the planet's life during which the communicating civilizations live. There is also a very nice calculator at the bottom of the following webpage (same page as above) that lets one plug various numbers into the Drake equation and see how many civilizations one gets. Link: http://www.activemind.com/Mysterious/Topics/SETI/drake_equation.html Finally, regarding the poll, I voted yes, for probabilistic reasons.

Actually, they leave the room for a very good reason. Think about it for a moment. When you go to the dentist and have a diagnostic x-ray of your teeth made, it is most likely the only time during the year that you are exposed to a relatively high amount of x-ray radiation. However, for the dentist, you may be their 3rd patient that week. Thus, if they stayed in the room when all of the patients have their x-rays taken, they end up exposing themselves to much higher amounts of radiation over the course of a year, increasing their risk for cancer.

Have you taken a Geometry class as of yet? If you haven't, you might want to consider the following definitions before you continue down the whole 'everything has a size and shape' path, for I believe the definitions below show that, at the very least, your assertion does not apply to Mathematical constructs. (The definitions shown below are from Wikipedia.) Point: "An entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured." Line: "An (infinitely) thin, (infinitely) long, straight geometrical object, i.e. a curve that is long and straight." That's not exactly correct. In colloquial terms, Calculus deals with 'the infinite and the infinitesimal', and was invented over 300 years ago. See my above response. Of course those who are familiar with Calculus may find fault with my above description of it, however, there are other fields in Mathematics ([math joke]No pun intended. Well, maybe just a little one. [/math joke]) that deal with infinity and infinitesimals in a more concrete manner, such as Non-Standard Analysis.

Yup. The nontrivial solutions are primarily what one's interested in.

Always try to work with round numbers, and split up decimals into more manageable parts. For example, say you wanted to purchase 5 items that are $1.17 each. Now, you could try to work out $1.17[math]\cdot[/math]5 in your head, but let's try another way. Now, we know that 5[math]\cdot[/math]$1.00 = $5.00, so keep that in mind. Also, $.17 is not a very round number, so let's use $.20, which is $.03 off. Now, we know that 5[math]\cdot[/math]$.20 = $1.00. So our "guess" is $6.00. However, remember we were $.03 off on each item, so we need to correct for that. So, how much are we off? Exactly 5[math]\cdot[/math]$.03 = $.15. Thus, we will pay $6.00 - $.15 = $5.85.

This is going to be rather unenlightening, but unless the equation is of some surface or function that I'm familiar with, I just see the equation, same as you. I don't. It would be cool if people who studied Mathematics had "Math-O-Vision", a la Numb3rs, though. Nope. Not me anyways. Yup. When I see a problem (in the ideal case), pattern recognition kicks in, and the relevant techniques to solve the problem are recalled from the recalled from the dark recesses of my mind. Of course, when one is working out a proof, this process takes a lot longer than a few moments. For example, a single proof of what I consider to be average difficulty will take me about 15 - 45 minutes of straight thinking, nothing else mind you, just sitting there, trying to get the idea for the proof. However, this is the single most difficult part.

Nope. Here's a nice introduction to matrix inversion methods. Link: http://home.earthlink.net/~jimlux/radio/math/matinv.htm

It may just be the pessimist in me, but if the above scenario were to occur, I would think that the poor would be used as cheap slave labor, since they would most likely be significantly cheaper that robots. Thus, since the rich actually have a vested economic interest in keeping the poor around, the poor are never eliminated from society, and the "everyone is happy" stage is never attained. EDIT: Regarding the poll, I voted "Yes", however, I think that the poll should distinguish between therapeutic and cosmetic genetic modifications. For example, if parents knew that their child would be born with cystic fibrosis unless genetic modifications were made, I doubt that many of the forumites would disapprove of such a procedure, if the potential errors/side effects of the treatment were fairly mild, or had a relatively small probability of occurring. However, one might question the motives of parents who elect for cosmetic modifications such as hair and eye color, since, as with any medical procedure, there is a non-negligible probability of a serious error occurring. In short, I voted 'Yes' because of the first reason, and I would never approve cosmetic genetic modifications for any future unborn child of mine. However, I don't think it is my place to tell other parents what kind of elective surgery their child can have. As long as it is approved by a qualified medical professional, they should be able to do as they wish.

[math]log[/math][math] 1=0[/math], so dividing by [math]log[/math][math]1[/math] is invalid.

We could use Calculus techniques to compute the area, but I don't suppose that you want us to use them, right?

Nope, we're trying to prove that [math]a \leq b[/math]. Suppose you wish to prove something of the form [math]a\implies b[/math] (in your problem, [math]a[/math] is "[math]\lim_{n\to \infty}a_n = a[/math], [math]\lim_{n\to \infty}b_n = b[/math], and that [math]\forall n \in \mathbb{Z},[/math][math] a_n \leq b_n[/math]", and [math]b[/math] is "[math] a \leq b[/math]"). Proofs by contradiction 'assume' that [math]\neg (a \implies b)[/math] is true, which is equivalent to assuming that [math]a \wedge \neg b[/math] is true (I use the [math]\neg[/math] symbol for 'not', and [math]\wedge[/math] for 'and'.). Thus, if by assuming [math]a[/math] is true and [math]b[/math] is false, we can show that [math]a \wedge \neg b[/math] is false, then that implies that [math]\neg (a \implies b)[/math] is false, which means that [math]a \implies b[/math] is true, which is what we originally wanted.