Shadow

Yeah, I believe Maple gave me something similar. Anyway, the notation I'm using is Knuth's up-arrow notation. And why can't I treat a Power Tower like I would [math]a^n[/math]? I mean, if we have a power tower [math]a \uparrow \uparrow b[/math] and treat it as [math]a^n[/math], then [math]a=a[/math] and [math]n= a \uparrow \uparrow (b-1)[/math]...doesn't it?

I did look, but I completely missed that page, so thanks for pointing it out. Another question, it say that in base 2i one can represent every complex number using only the digits 0, 1, 2 and 3. What about irrational numbers, such as [math]\pi[/math] or [math]e[/math]? Cheers, Gabe

Hey all,

Okay, don't have a clue what you're talking about, so I'll just accept it's beyond my grasp for now But thank you for all your help and patience, all of you. Cheers, Gabe

Hey there, First of all, I'm completely new to calculus in any form, so please excuse any completely obvious errors if there are any. I was just wondering the other day about the derivative of a Power Tower. I tried to treat it as [math]ax^n[/math], and came up with [math]f(a, b) = a \uparrow \uparrow b[/math] [math]f'(a, b) = (a \uparrow \uparrow b) a^{(a \uparrow \uparrow [b-1]) -1}[/math] Is this correct? Cheers, Gabe

Yes, I'm talking about actual impact. Although not of a planet with a star, but of a star with a star... I guess I'll just make the star "swallow" the planet if they ever meet )

The bouncing part didn't occur to me...the way I though about it is best illustrated like this: I know that's not what it would look like if a situation like this would arise, but you get the idea. Anyway, I guess that's just one more reason why not to use that method. What about doing what you mentioned earlier; treat the stars as balls of water, or alternatively gas... Anyway, I'm open to suggestions. Cheers, Gabe

Isn't this the same as asking how a line with negative/imaginary length looks...?

Not exact? Oh... Okay, I guess that gives me an idea of how hard it could be. I was thinking about "modeling" the stars as a bunch of particles, that just can't be broken down to anything smaller, and then just let those particles interact. Unfortunately, I'm not sure that would be computationally feasible, and to be quite honest I'm not even sure on how I would program something like that. What would you recommend?

It's the modeling part that confuses me. Again, this sounds like the exact way to do it. Isn't there some other, less complicated way? I think the Newton/Einstein metaphor summed what I'm looking for quite well. But thanks for your help anyway guys! )

Thanks iNow I read the posts, and I understand them. But surely I need more than this...if only because I don't see how all I've just learned ties into modelling a star as a ball of hot water )

So, what you're saying is learn calculus and come back? Do you think you could give me some leads as to what to study after I learn calculus? Sites, articles, lectures, anything. Even just an example or two of what I should do next, or maybe a list of things I should study. But thanks anyway, at least I have a specific reason to learn calculus... )

High school, not calculus though, which I believe is the seriously limiting factor here. Apart from that, it's sort of varying, since I do some learning by myself, and I can pretty much learn most of what I need. Or I have been able to so far ) As for physics, I'd say none at all, considering the teacher we have I just learn what I need to when I need to. In this regard, I consider physics to be a subset of math, as in "If I know the math part I can learn the physics part" which, again at least so far, works. I don't expect it to be trivial, which is why I'm looking for something like a shortcut instead of a full blown set of equations. Then again, I don't know if something like this is possible, and if it is, I don't know if it's in my grasp.

Well, as of three seconds ago I know something like that exists ) a quick google search just turned up a bunch of companies... What exactly do you mean by "model a star"?

Hey there all, I'd like to try and make a program that simulates 2D celestial collision (star with planet, planet with planet, star with star, etc.). Now, I know that something like this is probably impossible to simulate precisely, and if I even wanted to get close I'd have to call in some serious computer-power favors at NSA, but I'm not looking for something I can sell NASA. I'm just looking for an approximation. Could anybody here tell me what I should read up upon, which topics I should become familiar with, what kind of math/physics knowledge I will be needing, different approaches I can try, etc.? Again, I'm not looking for a precise way to simulate a celestial collision. I'm sort of looking for something that is to 'precise celestial collision simulation' what Newtonian Mechanics are to Relativity; not exact, but good enough. Cheers, Gabe

I know, that was what I though, but I though a bijection (ie. a bijective function) must exist between the two sets. My question is, what's the function in this case? Is something like [math]f(P_n)=n[/math], where [math]P_n[/math] denotes the nth prime enough? Is this considered a bijective function? And how does one know the reals can be put into a one-to-one correspondence with the power set of the naturals?

And why does it have the same cardinality as the powerset of N? I mean, why is |R| equal to all the combinations you can make with naturals? Is there some reason or is this considered something like an axiom? Just to clarify, I was giving myself a primitive test; the cardinality of odd naturals is also the same as naturals. If we add up even and odd naturals, since they're (I forgot the word, it means that they don't have anything in common) we unite them, resulting in N. It makes sense... Also, how can Primes and Naturals have equal cardinality? I mean, what is the bijective function in this situation? Cheers and thanks a bunch, Gabe

Well, I did a quick read on wiki (btw, I know what sets are, I just didn't know the English word) and the even/natural thing makes sense, however I don't have the proper knowledge to understand most of it (the whole ordered set thing is completely beyond me, but I didn't really try to understand ). Just a quick question, why is the cardinality of R defined as [math]2^{Aleph_0}[/math]? Cheers, Gabe

Ah, I see now. My bad. Thanks for explaining guys ;-) Cheers, Gabe

I know they have the same number of elements, that's my point. I'm just not understanding how that can be. I'm not familiar with sets, so I'll use a metaphor. Say we have a house and in it an infinite amount of room. Each room takes up the same amount of space, and each room takes up the same amount of space as all the others put together. How can this be? As for the multiplication thing, I don't exactly know what transfinite cardinals are, but I have an idea. Anyway, the multiplication was just illustrative. I just wanted to express what the above metaphor does. Cheers, Gabe

Yeah, I know, [math]2\infty = \infty[/math]. But from a logical point of view; the number of reals between 0 and 1 is x. The number of reals between 1 and 2 is also x. So the number of reals between 0 and 2 should be 2x. Thus, the number of real between any two reals a, b should be |(a-b)|x. How then can the number of reals between 1 and infinity be x? Cheers, Gabe

If [math]\sqrt{-1}[/math] is illegal, how can [math]i[/math] be defined? I told you, no Czech; only English

Hey all, another post just reminded me about this, and I've been wanting to post it for quite some time. However, math syntax and me don't go together, so excuse the errors. Let us have a function (I'm using different brackets so they don't get confused with part of the interval) [math]N[x][/math], where [math]x[/math] represents an interval, and [math]N[x] =[/math] the number of real numbers in the interval [math]x[/math]. I know it will always be infinity, but bear with me. Let [math]a_n= N[ <n; n+1) ] \Rightarrow N[ R^{+}_{0} ]=\sum_{n=0}^{\infty}a_n[/math]. [math]\forall x \in R: x \in <1 ; \infty)[/math] [math] \Rightarrow 1/x \in (0 ; 1>[/math] [math]\Rightarrow N[ (0 ; 1> ] = N[ <1 ; \infty) ][/math] [math]\Rightarrow \forall z \in Z^{+}_{0}: a_z=N[ <1 ; \infty) ] \wedge a_z=N[ (0 ; 1> ][/math] [math] \Rightarrow N(R^{+}_{0}) = 2a_z[/math] [math] \Rightarrow \sum_{n=0}^{\infty}a_n=2a_z[/math] which is not true. How is this possible? Cheers, Gabe

Hey all, Where am I making a mistake? [math]-i=(-1)\sqrt{-1}=\sqrt{(-1)(-1)(-1)}=\sqrt{-1}=i[/math] Cheers, Gabe

I don't know, I think I'll always be a FF user, or at least as long as I don't see articles popping all over the net talking about how incredibly faster and better it is than all the other browsers. And frankly, I think that will take quite some time. Cheers, Gabe