Bignose

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1. Quantifying a process

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

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?
3. Beginner in mathematics, i'm studying alone.

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.
4. Needing irrational help

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?
5. Axioms, definitions, and 0.999...=1

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.
6. Axioms, definitions, and 0.999...=1

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.
7. Axioms, definitions, and 0.999...=1

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.
8. rational/rational=irrational=π How?

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 $\sqrt{2}$ which is also an irrational number.
9. % problem

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?
10. I hereby challenge Relativity and promote Aether.

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.
11. I hereby challenge Relativity and promote Aether.

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?
12. I hereby challenge Relativity and promote Aether.

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.
13. I hereby challenge Relativity and promote Aether.

Shocking or not, it works. See https://arxiv.org/abs/1403.7377 (You know, the link I posted in the 1st page of this thread that seems to have been forgotten about.) It is 113 pages of just how damn close the predictions from relativity agree with physical experiments. Until you are prepared to show us how every one of those examples is wrong and you have an idea that can make better predictions, snappy quotes and promised gifs are meaningless. This is how science works. Put up or shit up. Put up by actually showing us your theory in mathematics and how good its predictions are. If you can't, then you need to drop all these claims.
14. Infinite coin flip probability

Not when you give me infinite flips. With infinite flips, a symmetric random walk on 1-D will visit every point. It doesn't matter where you start. Given infinite flips, it will visit every point.
15. Blasphemy (Aether, really)

you can think what you want, I guess, but the fact they they work as they do is validated over and over and over every second of every day. Like, airplanes take off, cars work, the electricity that is powering the device you are typing this dreck on works, the satellites that make GPS work, etc. etc. etc. Conservation of energy -- and the equations for the known different forms of energy -- are among the most validated equations we have. Maybe the single most. Your personal opinions on them are not worth the electrons it took to display that on my screen. In short, it is going to take an awful lot of extraordinary evidence for such an extraordinary claim. A helluva lot more than just a thought experiment. I shall not be holding my breath waiting for you to provide some given your history of making claims and not being able to substantiate them.