Bignose

Did you guys all forget that this is a discussion forum? The OP starts a thread on a forum, by definition, because they want to discuss something. Then OP in a matter of a very short time says (paraphrasing) "well, actually I can't discuss it". So... if there isn't anything to discuss, why are we surprised that the thread was closed? There is little need to document everyone asking questions and providing critiques that OP has stated they cannot or will not answer. Thread closure is the logical next step; if there is to be no discussion, then there is no point on a discussion forum.

If all 11 variables and all experiments are independent and identically distributed, then you can use the binomial distribution to calculate what you need https://en.wikipedia.org/wiki/Binomial_distribution

And what I'm saying is that no equation can ever give you something correct if you ask the impossible... There is no correct equation to tell you what the odds are to do something impossible, in your case it is impossible to draw more cards than what are left in the deck. If you are programming this in a system somewhere, you need to check the inputs to limit the calculation only to actually feasible scenarios. If someone asks the impossible, you return an error, or 0, or a message explaining the impossibility, or whatever is appropriate to your system. You're fundamentally asking of the math an question it cannot answer. It is like asking 'how heavy is the color blue?' or 'how many candle lumens in a hogshead?' or 'how do I pay a $100 electricity bill when I only have $15 in my account?' Math is not the solution to impossibilities.

Well, sure. The math says something is wrong when you attempt the impossible: to draw more cards from the remaining deck than are in the deck, H > (D - T). Its no different than asking what happens when you try to lift a boulder with infinite mass or try to divide by zero. The fact that the math can't be done indicates that you're asking for something impossible and you need to check that what you've set up the problem to do is correct.

I think your investigation should begin with studying the spherical coordinate system: https://en.wikipedia.org/wiki/Spherical_coordinate_system Understanding that will go a long way toward answering your questions.

1) I am specifically asking WHERE the 'center' of a vector is? Because you need to know where that is before you drag anything through it. I have never heard the term 'center of a vector' before, and just wanted to understand. As near as I can tell, this is term you made up and didn't bother to define. 2) no need for name calling. Just asking a question. If you are going to name call when someone asks a question, then expect your time here to be short.

Was this supposed to address wtf's comments? Because not only have you failed to define what is meant by 'inverting a sphere' you introduced another meaningless mathematical term -- the center of a vector. Please define both of these terms explicitly.

no. not ok. Firstly, this is a forum. Everyone who follows the rules is allowed to post. Secondly, it is just advice. It is worth exactly what you paid for it. Feel free to take it or not. I am simply trying to help you by showing you the tools that, well, every other person who does math uses. Again, if you have ideas on a certain subject, it usually helps to learn the terminology and language of that subject. One would think that being able to better describe an idea would be a good thing. But hey, you do you. Do whatever you want.

then, mathspassion, you need to go and learn some algebra. Because the 'proof' is simply variable manipulation. If your namesake is true, and you have a passion for maths, you should be trying to learn as much of it as you can. And algebra is a very fundamental building block of math. Not only that, but if you learn algebra, you'll be able to express ideas -- like the one that started this thread -- into a more succinct and generally understandable format. Strange was not the only one who struggled to understand what you were trying to say. Learning the terminology and nomenclature that you will learn in algebra will help you convey your messages much, much easier. It is worth the effort.

Dude. Just multiply it out. This is like basic algebra. Post here if you need help, but if you just expand each term on the right hand side, you'll see the terms cancel and prove the identity.

So... you've converted 1 number lookup (the N) and 1 multiplication (N*N) into 4 number lookups (have to find the numbers on the square snake thing), 2 multiplications, and 1 addition. I guess I fail to see any practical reason for it, tho that has been said about a lot of math.

I didn't think that there was much mystery about Buffon's needle, except the fact that so many so-called 'real world' experiments of the problem ended up just a little too perfectly in line with predictions many, many times throughout the years. In my opinion, if you want something that is a bit more mysterious, check out Bertrand's paradox. https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) It is my favorite example of 'probability requires you to be extremely careful in your definitions'

272 integer results... do x, y, and z have to be integers? The original problem statement did not state that.

Um, 1200-980 = savings of 220? If it cost more to get two quotes, then that comes off the savings.

How do you handle the fact that there are mathematical proofs that there is only one unique zero that obeys the axiomatic rules for how a zero operates?

So, the forum is usually happy to help, but will not just give you answers -- just getting answers will not help you learn. What have you tried to do to solve these yourself first? Post the work you've done and the forum will help correct or guide when you get stuck.

Do you have any concept of how many times in any given day, the value of pi is used? This 0.1% difference would result in so many things going wrong. We're talking about: satellites falling out of orbit, GPS not working correctly, every single Fast Fourier Transform algorithm returning wrong results, every single calculation of the trig functions returning wrong results. How can all these be wrong and yet seem to be working so well?

The first 'paradox' you have to get over then is trying to understand 0.99999... and the natural numbers. The naturals are just just the positive integers. Once you write that decimal point, you've already gone outside the bounds. Secondly, the concept of an inequality is axiomatic. And what I wrote above comes directly as a consequence of using that axiom on the set of reals, not natural numbers. On the reals, and the limitless amount of numbers that can be found between any given two numbers that aren't equal (which comes directly from the definition of the reals) you can always find a number between them. The c in the a > c > b I wrote above. So, if 0.9999... (just to be clear, the ... means infinite 9s) does not equal 1, what is the c that lies between them? 0.999....1 is meaningless because you've already stated INFINITE 9s. It is as meaningless of a number as 'dog leg' or 'flooblie' or 'sasquach'. Sure, you can write something down there, but it has no meaning. Or, use your own phrasing here, 0.9999....1 isn't axiomaic because none of the accepted axioms give any meaning to something written in such a way. In much the same way that starting with the natural numbers, 2.3 has no meaning. The natural numbers do not know what a decimal point is; it is against the rules you started with. There is no rule for the reals giving any meaning to 0.999...1 In short, you need some clarity on defining your problem and your terminology. Because we're trying to answer it as best we can, but you're not playing along with the rules you've tried to set out.

I like to think of it simply as another way to write the same number. Like 6/3 and 2 both represent the same number, just written in different ways.

If we know that some a does not equal b (let a > b), then there always exists some number c such that a > c > b. If 0.99999... is not equal to 1, what is that number that comes between them? I have never seen someone who 'doesn't believe' 0.99999... = 1 give any kind of meaningful answer to this.

Hi Eren, welcome to the forum. It is NOT two rational numbers being divided. That's actually the definition of an irrational number, there are no two numbers that we can use in a ratio or division to make that irrational number. https://en.wikipedia.org/wiki/Irrational_number However, a good example of two rational and measurable numbers 'making' an irrational one is a right triangle with the two sides next to the right angle having length one. The hypotenuse of that triangle will have length [math]\sqrt{2}[/math] which is also an irrational number.

Imagine a school classroom of boys and girls. If 50% of the boys won medals at the annual sports day and 75% of the girls won medals at the annual sports day, do you really think that 125% of the entire class won medals?

What's really not fair is you showing up and 'hereby challeng[ing] relativity' when you admittedly don't understand it and are ignorant of the literature around it. This would be like saying 'I don't understand the equations of fluid mechanics, therefore I hereby challenge airplanes' and bitching when someone talks about Navier-Stokes (the most famous equation in fluid mechanics). The onus is on you to understand and know a subject before you shoot your mouth off and challenge it. The obviousness of the error is that you can't make predictions that agree with experiments. Again, this would be like saying airplanes can't fly. While watching them take off behind you. There is excellent agreement between relativity and experiment. Just because you don't understand it, doesn't mean it's wrong. Appeal to ignorance is a logical fallacy. Look, I agree it is some complex math. But the truth is it works. You cannot deny that. In science, you may not always like an idea, but dammit if that idea produces good results, you don't get to just hand waive that away. You have to accept that if your idea cannot make more accurate predictions, that your idea is inferior. Period. Full Stop. No More. Once you get that, then the onus is on you to go back and remedy the error, if you choose to do it. You don't get to just claim that your results are better. It is an objective measure: predictions that agree more closely with experiment is better.

You don't have to do any experiments. They are done for you. See the paper. See the references therein. The experimental data is already out there. At the very least, if these experiments can't discriminate between your idea and relativity, your idea should make predictions at least as good as relativity's predictions, right? If not, then your objections don't mean squat as best predictions win in science. So show us that. Or maybe anything other than a vidya and stories. This is a science forum, after all. How about actually doing some science?

Reality, yes, let's get back to that. Again, when are we going to see a comparison between whatever predictions you make and reality? E.g. https://arxiv.org/abs/1403.7377 Stories and YouTube videos and words are all meaningless. Show us that your predictions are better than relativity's. Full stop.