Note regarding all of the above: To a certain extent, each of these arguments depends on a basic foundational doctrine of mathematics called "The Axiom of Choice". A discussion of the Axiom of Choice is well beyond anything we could cover here, and is something that most mathematicians simply take on faith. From your link. ^^^^^^ Get arbitrarily close, but never actual.
What he is talking about is 0.(9) Or 0.9999^infinite = 1. As putting the 9 as (9)...means to the infinite. AA
Okay let's start: (1) x=0.999... In this step we would need an endless time to write down all digits of "9" - instead of this we agree to write "...". If you should not agree no one ever will be able to discuss with you any longer anything because "Eternity is a long time - specially in the end", how Woody Allen said. (2) 10·x=10·0.999...=9.999... Same problem: We would need an eternity to move all digits one position left. The astonishing thing now. 9.999... has 1 digit more if we don't count the leading 0. But ∞=∞+1 or ∞=∞+n : With other words: wherever you are counting in an endless number of digits you are always able to count any limited number of digits more. By counting you are not able to count in a region higher than ∞. (3) 10·x-x=(10-1)·x=9·x= =9.999...-0.999...=9+(+0.999...-0.999...)=9+0=9 I guess that's very clear now. (4) 9·x=9 (5) x=1 (1)+(5) => 0.999...=1; Maybe your problem is that you trust in machines. But computers are very bad in mathematics. A programmer will prefer to write 1 instead of 0.999... because a computer has only a limited amount of memory. And in all calculations he will try to minimize the problems machines produce with their limitations. https://youtu.be/jVkN2WNOnuc
https://www.youtube.com/watch?v=SDtFBSjNmm0 Correction! I was wrong, and this video shows why. Lets take x=0.9999999999999999.... and multiply it by 10 on both sides.. 10x= 9.9999999999999999... That means that if we subtract on both sides... 10x= 9.99999999 -x= .999999999 9x=9.00000000000 9/9=1
Guys, let's put a point. ------------- The decision, written by me, - it is an axiom of mathematics A = 1 B = 0.9999 ... = 0, (9) ====================================== These numbers are equal .. Teach Math .... ============================== Dot.
Actually if we formally use the multiplication algorithm to multiply 9 by 0.999…, (9x), the result comes out to 8.999… which is not the same as 9. These are not true real numbers and formal math acts badly with these types numbers so mathematicians basically ignore and claim 0.999... = 1 and couch it in spiffy language. The real question is what are real numbers in the first place? Infinity is a math trick and plagues many calculations.
8.999... = 9. That's the same. If you read again and think about what I wrote, then you know very well why it is exactly in this way. The only problem is to understand rules like ∞=∞+n and ∞=n*∞. You should not forget: To calculate and mathematics are different things. Machines are calculators and not mathematicians. Machines are not able to think. That's why we sometimes get stupid results with computers. https://youtu.be/yxlEojkVJ0c
8.999... = 8 + 0.(9) = 8 + 3*0.(3) = 8 + 3* 1/3 = 8 + 1 = 9 ------------------------------------------------------------------- infinity has nothing to do with it !!!!... It's simple math ... ---------- It called in the USSR - arithmetic .. Soviet students such questions solved in the 7th year of secondary school (13-14 years old)
Who accepts not that 0.999... (or 0.(9) how you write) is 1 accepts also not that 0.(3) = 1/3 - that's the same logic. Why do you write this to me? https://youtu.be/Yn9bFBonY3Q
never hesitate to forums Cossack song in German ... It is laughable ... --------------------------------------------------------- remove and do not disgrace
Mercy. But I have nearly nothing to do with. I'm only messenger - the message comes from someone else. https://youtu.be/91-J6bf6QsM
remove the link that I have suggested ... Offline many immigrants who speak in Russian .. ------------------ that link to Russian looks very funny ... ============================== oooo .... this is another link. Very good I love this kind of music! ============================= ==================== You're from western or eastern Germany?
very good music.. ---------------- These guys are who? Perhaps Scotland ... ----------------- I say in Russian, English, Suomeska, Udmurt ... But I did not understand their language
