MandrakeRoot

Isnt the whole point of what you are trying to do : approximating the lambertW function with some complex number ? Analytical expressions would simply give x = -LambertW(-1) as a solution. have you tried using command line maple also ? evalf(-LambertW(-1)); ? Mandrake

How about using evalf or something like that ? That is a long time ago i used maple but i think that is a valid command right ? Mandrake

In fact i used the so called Lambert W functions, the property of this function W(z) being W(z)exp(W(z)) = z; Taking z = -1 here will gives a solution to the original equation, being x= -W(-1) =(approx) .318 - 1.337 I I think this is the only solution. Mandrake

There is a unique solution : approx : .318 - 1.337 I Mandrake

Yeah i know that. It was not the point i was making. Must have explained me badly i guess.

Let me remind you that the argument of -1 is pi ! It is always the best to specify which branches you are using when using complex functions (with branches), since otherwise you are omitting something in your argumentation. I will emphasize again that the goal of the post was to show that using notations that have a specified context in another context can be dangerous, since you can not blindly apply the same rules ! You can't calculate with the complex sqrt function as easily as you can with the classical real sqrt function. Mandrake

Yeah without specifying this sort of stuff; meaning it is not the same sqrt function ! That is the whole point of my post, that you cannot use this as the classical sqrt function. So NO the notation doesnt have a sense when you do not specify with branch you are using. Mandrake

This is straightforward showing the three rules hold. Let me do one : a ~ a, since a -a = 0 is integer If a ~ b, then a-b is integer, hence -(a - b) = b-a is integer, thus b ~a finally if a ~b and b~c , then a - c = (a - b) - (c - b) is integer by the above and the fact that a ~b and b~c , so a ~c. IT is really easy Mandrake

Dividing by zero is undefined and cant be defined, since such an operation or notation would not have the normal sense. 1/x is a short hand notation for [math]x^{-1}[/math], the unique element in [math]\mathbb{R}[/math] s.t. [math]x^{-1}x = xx^{-1} = 1[/math]. If you want to give a sense to 1/0, in no way it would be the inverse of zero thus making this notation totally superfluous. The same holds for your argument 123rock, since like i just said, no way 1/0 will be the inverse of 0, so your argument with x and 0/0 is nonsense. Another exemple : Often people write [math]i = \sqrt{-1}[/math], where i is the complex number. This notation also has no sense. I will let you guys try to find the error in the following reasoning and see for yourself why it is meaningless to write [math]i = \sqrt{-1}[/math] : [math]-1 = i^2 = (\sqrt{-1})^2 = \sqrt{-1}\sqrt{-1} = \sqrt{-1 -1}= \sqrt{1}=1[/math] Mandrake

Yeah i know we need numbers to have a common framework, in order to talk of stuff. I was just wondering if a primitive culture could find out also by experimentation that something could take forever, without any number reference. Too bad In set theory it is possible to add to any partially ordered set, a biggest element, this element can be called infinity if you like. It is exactly these properties that "infinity" has for the "extended real line", it is the biggest element in this set under the well-ordering <=. Dividing by zero is utter nonsense 123rock, it is impossible to define such operations rigorously without contradicting yourself. Mandrake

No in fact he even said that time was finite too ! Thats pretty silly... Just thinking, how do we mesure time without making reference to numbers ? Hourglass to mesure discharge rate ? But how would we express it without numbers again too ? It would be great to have an exemple which could be verified without anything to count/ reference to a number system, that would be the ideal "practical/real exemple" i would say. Mandrake

That is a cool exemple. Is it possible to show it with some measurements that it would never discharge completely ? Mandrake

Though you can represent recurring numbers with only a finite number of them I dont think this DrBelfrey could write down pi with only a finite number of decimals, though following his arguments he should be able to . I think it is more hard to find an example of infinity without referring to numbers/math constructions though ? Any idea ? Mandrake

Dont you mean the proof that the set of real numbers is actually bigger than that of natural numbers. Meaning there are different "degrees" of infinity, i.e., Both sets are infinite, but one is actually bigger then the other. The size of the natural numbers, its cardinal is called [math]\aleph_0[/math] and the cardinal of the real numbers is [math]\mathfrak{C}[/math]. Mandrake

I have tried to read your first stuff (the part on Non-Naive math) on your page, but it is rather confusing. You should really write it down more clearly because it is written down rather chaotically. Cant you write like : introduction =>definition =>Theorems (or whatever the equivalent in this new logic, it should have statements anyway no ?) So in this logic of yours (True and False) is a meaningfull statement ? And (True and False) and (True and False) is another statement not necessarily the same outcome. When you say that each interval has the same cardinal as the real line you are using old set theory results that do not yet exist when you are creating new set theory ! Moreover in no way that means that the real line is this interval, one can not exist without the other, i mean the interval has the same cardinality only because the real line exists ! The same is true for scaling. Yeah ofcourse the real line can be obtained by arbitrarely rescaling pi, but well the real line has to exists forthat, since you need these scalars to obtain it. Why in your system are the set of odds numbers not equally sized as the set of natural numbers ? Mandrake

The entire power of MAth is this concept. Once somethign is defined everybody knows what you mean when you use it ! e.g. Once i defined what is a continuous functino there is no doubt for anyone what i mean when i say a function is continuous ! How could you possibly want to do something other then that ? The whole goal of science is to make results/things insightfull ! Science has to be reproductable and understandable to other people then yourself ! people should be able to verify your results ! If your stuff doesnt submit to these criteria then it is not science ! I will actually try to read some of your stuff to see if i can make some sense of it. Mandrake

Yeah can't you write down for exemple the two pages of your first axioms clearly ? On the second page of this PDF you start talking of directions without defining it, i somewhere have the idea you try to define stuff that you assume already exists using properties of the stuff you try to define in order to define it. Some clarity is needed please Mandrake

Yes you are right that the platonic point of view is an opinion but a pretty beautifull one. If you think of it, it is not at all that stupid. Any theorem is some statement that is true, logic if you want. The statement is true whether we have written it down or not so well the theorem exists. This has nothing to do with "power over nature" though, since it is more something about a universe of concepts or whatever. Nature is real and we are part of it, so is the Hahn Banach theorem. Our theories allow us to understand nature and not to control it ! Science is not inherently tied to "power of nature", but often is <b>used</b> for this purpose. Pythagorean theorem is not the same as its use. The source of energy you talk about can exist without pythogorean theorem and vice versa. Mandrake

Zelda also uses an Hit point system in the form of the hearts or whatever. If you really want to play a good RPG, play AD&D with some friends, the real game i would say. It is a lot of fun since normally it is a game without any bounds, you can do whatever you want in it. In Gothic II you have direct control over the weapon i think. So there are surely RPGs on the computer that give you some control. But hey even in the original Zelda you didnt have control of your weapon. You could basically poke and that was it. Mandrake

In fact the theories exist without us, it is just that we have to realise they do ! Well anyway that is some point of view about theorems and lemmas etc.... Ofcouse we have to use the theories we have developped for the best use for everybody. I am sure nobody will disagree with you on that, it is like a universal truth ! I would say like e(... That the theorems are not "immoral" or anything, they are just statements, like a sentence. Everybody that uses them will use their own morality in order to judge whether or not the outcome of his work will be worth while... So in fact it would suffice that all scientistist are moral beings, doing all for the better of the world right ? I still dont catch why there should be morality in theorems like Hahn-Banach or Pythagorean theorem ? These are abstract statements.... Morality should help though in the search for food e(...) normally that should prevent us from putting 1.000.000 chickens in a 10 square meter cage or cutting their beaks because they will hurt each other ! (Hey i would too if i would be stuck in 10 square meter with so many other people ) But then again science has nothing to do in this judgement, theoretical science is without morality, it is the application where morality is desired in order to "create" "correct" things. Mandrake

Many wars have been the result of fear or Jealousy or other human emotions and not technology. Even in the time we were fighting with swords the wars were pretty gruesome. Secondly i disagree about the fact that universities do not teach there students about "moral" issues. Many of them have included obligated courses of Sustainable developpement and other courses allowing students insight into what their "discouveries" might create. Moreover why should we use "morality" in for exemple Hahn-Banach's Theorem or Riesz representation theorem ? These are abstract theorems and abstract maths costs only paper (if you sustainably cut wood this should not pollute ), the problem is applied mathematics for any technologic developpement that may pollute a lot (or kill everybody or whatever). So my point here is that it is not the math system that is immoral but those that use it for "bad" causes ! Mandrake

I always loved playing AD&D with friends, it is a great game. In computer RPGs most D&D based games are pretty cool. Never played Diablo though, but seems like hack and slash to me. Doom doesnt really seem like RPG either since well the main part of the game is to blast the shit out of the enemy, doesnt matter how as long as it is dead right ? (Can be fun though) Normally RPGs should have interaction with folks and many stuff other then combat, the entire fun is often to play with friends (in the non computer setting ofcourse) and to let the characters interact and whatever Mandrake

Well it depends a little what domain of the function you consider. You didnt specify so well i just gave you the first solution that came to mind. If you restrict t and x to some cube this is a perfectly square integrable solution. Mandrake

For every [math]\sigma \in \mathbb{C}[/math], [math]\phi(t,x) = e^{\sigma(t - \frac{1}{c}x)}[/math] is a solution to your equation. Mandrake

I still dont see why 0 1 reasoning will lead to destruction of the world. We are seriously polluting the world because we are stupid and not because we reason 0,1. This is by the way a very natural reasoning methinks, and doenst exclude any moral reasoning at all. Like e(... says you are probably just looking for another set theory. Mandrake