# MandrakeRoot

Senior Members

194

1. ## What are your Fav Theorems.

Hey thanks. Thought it could take the text also. Mandrake
2. ## What are your Fav Theorems.

Yes bloodhound, it does indeed Mandrake
3. ## What are your Fav Theorems.

If $z = rcos(x) + irsin(x)$, then $z^n = r^n \cos(n x) + i r^n \sin(n x) \; \forall \; n \in \mathbb{N}$ Mandrake PS : why my math formula doesn't show up ? The only thing to do to have full LaTeX use is to write [ math ], [/math ] around the LaTeX code right ?
4. ## What are your Fav Theorems.

Hey how do you guys make the math signs ? Mandrake
5. ## What are your Fav Theorems.

I think the statement of the moivre's theorem is : If z = rcos(x) + irsin(x), then z^n = r^n \cos(n x) + i r^n \sin(n x) for all n \in \mathbb{N} Mandrake
6. ## What are your Fav Theorems.

That is not a theorem either, but more a direct result from an identity exp(i phi) =cos(phi) + i*sin(phi) Mandrake
7. ## What are your Fav Theorems.

Euclids parallel postulate is an axiom and not a theorem. I would say Riesz's Representation theorem : The dual of every hilbert space can be isometrically isomophically embedded into itself. Mandrake
8. ## Programming Excel to Calculate Pi

How about using a cell and writing =ACOS(-1), that gives you PI also, until whatever decimal precision that excel uses, probably enough for your calculations Mandrake
9. ## Using theories and proofs. Why couldnt there be an end to numbers?

I dont quite understand your question ? But there is a simple set theoretic construction allowing you to add a maximal element to R, the set of all real numbers (keeping well ordering and all) Mandrake
10. ## Limits of "cyclometric" functions

Bishnu, the problem with your reasoning is that you are using the taylor developpement around zero and then you fill in 1/x, but what you basically would need is the developpement at infinity. Which is 1/2 Pi - 1/x + 1/3 1/x^3 - 1/5 1/x^5 + .... filling in 1/x, and multiplying with x gives you an expression with only x's, so taking the limit gives 0 Mandrake
11. ## Help : Transfinite Numbers

Could you clarify your question a little bit better ? Mandrake
12. ## Homosexuality = genetic defect.

Here couldnt is a mental impossibility, not a physical one. Clearly physically a homosexual is just as much capable to reproduce (should he choose so !) as anybody else, but the point i am making is that if we define a homosexual as someone that is only attracted to the same sex, then there is no choice ! Never will he think of reproduction/sex with a member of the opposite sex, since the idea would disgust him/her. So he is mentally blocked to reproduce. I hope i am more clear ? So in the case of the definition i would say that cant=wont, couldnt=wouldnt Ofcourse you can imagine that some people might choose to have homosexual relations and then after again not etc..., but those would not be "real" homosexuals in the sense of the definition of not having a choice (in the sense of just being born that way). Mandrake
13. ## Some Hebrew Pi

If i am not mistaking the hebrew letters already carry a certain "load" (meaning) and the words are composed of those letters giving the meaning the word, like an addition of meanings. I completely agree with edward that you can make say Nostradamus what you like. I read somewhere once that he predicted the return of jesus in 2007 (we will see ) There was a guy that once wrote a poem in the style of nostradamus to show that you can make what you want out of it (before 2001) for some thesis or something like that. Later this verse circled the internet and journals to show that nostradams predictd the wtc attacks. I am rather sceptical about the hidden messages of the bible/Koran/Torah or whatever other religious book. It is the content that is important and not so much the words. Predicting the future would be by definition impossible i would say. Mandrake
14. ## Autoimmune Diseases

You are pretty young then ? It is good to have ambition, i hope you could realise one day the stuff you would like to do. Mandrake
15. ## Homosexuality = genetic defect.

I agree with admiral here. Evolutionary arguments are a little misplaced in this debate since the human race doesn't really seem to follow the strict rules of evolution Technically someone that needs glasses should have less chance to reproduce, as does someone that is less intelligent etc... However clearly that is not the case. So the human race sort of cheats on evolution (for the moment) and therefore i dont think that any such argument could quite "finish" the debate here. OTher then that if we define a homosexual as someone that is only attracted to the same sex (there is no choice element). Then no they cant reproduce since they couldnt mate with someone of the opposite sex. Why would "love" (whatever its definition) not be seen in the animal world ? There are species of birds that stick with the same mate all their life, clearly they must be driven by something other then just the need to reproduce here i guess. J'Dona , are you actually saying that more people there are, more of them are gay ? So countries with a higher population density would contain relatively more gay people following your reasoning then ? (I doubt that to be true though) Mandrake
16. ## Homosexuality = genetic defect.

Human behaviour is largely determined by the circomstances we grow up in, so there is really no way you can draw your conclusion that homosexuality is a genetic defaut. Thing is nobody knows why some people are homosexual and we probably never will. I agree that from a strictly evolutionary point of view it makes little sense, but then again it is just a theory. Human survival is largely due to our group nature and i am sure someone can come up with a nice speculation as to why the presence of homosexuals would strengthen the group in its survival ? Every "classification" of homosexuals as gentically flawed or suffering from a disease or whatever are all based on speculations, most of which do not make sense. Mandrake
17. ## Integration

If you would pose y(x) = x^2 it is even known that there is no analytic expression (in terms of standard functions) for the integral, other than int_0^x exp(z^2) dz ofcourse. Mandrake
18. ## a probability

Yes i partinioned Omega into two subsets to keep it simple Mandrake
19. ## a probability

No clearly not ! What is true is the following P(A) = P(A | B)P(B) + P(A | B' ) P(B ') (wet of total likelyhood) and where B' denotes the complement of B in Omega Mandrake
20. ## Do You Believe There is Intelligent Life Beyond Earth?

I would still call life that evolved on earth regardless of its origins terrestrial life, as long as they fit in with the environement. Since any species that evolves on earth would have an impact on the eco-system and be part of it, if it is here long enough. Then there presence effects others species that were here originally etc... Other then that the first cell-life forms were made of atoms that werent necessarily here when earth formed (maybe, but that is not perse needed), and other then that earth formed from material coming from out of space. So either we are all alien according to your reasoning or we are not because we co-evolved with the planet. Why would these deep sea fishes be extra-terrestrial ? Yeah i think there is extra terrestrial life in the sense of species evolved on another planet. Guy what is your point ? That aliens are apriori not looking like us ? But maybe there is a "winning configuration" as in one that can easily adept to almost any situation, that would anyway force some similarity in between aliens ? Mandrake,
21. ## Do You Believe There is Intelligent Life Beyond Earth?

I have no idea ? Isn't it english ? Anyhow "Miljard" is a dutch word, but that is not the same writing. Mandrake
22. ## Can a continous interval have a finite number of points?

Hi, I dont understand your definition of your function f ? If with 0.999999... you mean that this series of nine's continues indefinitely then it is the same point as 1, similarly if 1.000000000...1,means that you let the zeros continue indefinitely, then this is also 1. So you defined a function on a single point {1}, and well if you see f as a function from {1} into R, where you let {1} inherit the metric of R restricted to {1} it is a continuous function, though not very interesting. Remark that {1} is open in {1}. If you would consider the function f : [1 - eps,1+eps], with any eps > 0, defined by f(x) = x; then you could consider the restriction of f to (1 - 0.5eps,1+0.5eps) to have a(n) (open) neighbourhood of 1, and your function will equally be continuous. Mandrake
23. ## randomness in math?

Do you mean in mathematics or applied math ? There is a big difference you know. In math i would say no there is no randomness as every "random variable" is just a measurable function. In statistics or probability theory, properties of these functions are used to show that some estimator or something else converges to what we would like to have. In applied math the situations of the practice are modelled by random variables and this turns out to be very usefull. So in fact it depends of what you call "random" in "the real life" i guess as to whether or not randomness really exists in "nature" or if it is just a usefull model ? Mandrake
24. ## Do You Believe There is Intelligent Life Beyond Earth?

Hi, With mlj i meant milliard = billion. Sorry about the confusion. Even with a god argument the existence of extraterrestrial life would not be impossible. God could surely have been fed up of seeing us f**k it up each time he gave us confidence, or he just wanted to create another species that hopefully this time would not destroy his creation ? Or why would god create a universe so big, but really sooooooooooo very big compared to our small nature (on universal scale) and just populate one tiny little planet out there letting the rest a lifeless dessert ? Even the most inhabitable place on earth has life on it, if you think to it, so why would god not do that also in the universe ? mooeypoo what do you mean with alien life on earth ? If somehow bacteria arrived here and evolved into us (or something else), then it would be terrestrial life i would say, since lifeforms actually shape a planet and we would co-life on it since a long time already. Mandrake
25. ## Do You Believe There is Intelligent Life Beyond Earth?

I dont understand why would alien life (if it exists) necessarily be lesser life forms ? If you can define lesser ofcourse ! The whole concept of lesser life is ridiculous since you calculate it by a criterium that is something proper to our physiology. For exemple we call a dog a lesser life form because he cant write down math equations or in any case communicate his thoughts on math equations (purpose of life etc...) to us in a comprehensible way (for us again). But if we would have taken as a criterium finding stuff by smell then it would be us the lesser life form. So well the same thing would account for extraterrestrial life. If we wouldnt understand them, that wouldnt mean they are lesser ! I would say that it is highly probable that there are many life forms out there in many different stages of evolution, since if you look to it, the universe is pretty old (10 mlj years i think no ?), and our solar system is only 5 mlj years old, Earth is approx "habitable" since only 4 mjld years and life is here in the most simple form since approx the same time i guess, but well many setbacks have whiped out the entire population of animals in course of evolution. So the path to our evolution has been set in approx 65 million years ago, and we are here maybe since 100.000 years, which is pretty small compared to the age of the universe. So any lucky planet where life began in the same time as here on earth (but without the disasters) could contain life way more advanced (from whatever perspective) Since there are so many stars, there are probably many planets like ours (if that is needed for life?) and thus surely some that have known developments of evolution like ours. I dont believe in the UFO stories though ! Clearly "aliens" would not visit our planet and waste there time making circles in crops or stupid stuff like that. Could you imagine us doing that ? After years of research or in whatever way, we finally arrive to a planet habited by aliens (with all the technical difficulties of such huge space travels) and then we would stay hanging around, not letting them detect us and make circles in their fields just to amuse us ? Highly unlikely i would say ! What would be the argument against the existence of extraterrestrail life for those that dont "believe" in it ? Mandrake
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