then you can't multiply it by 10 either. because whenever you multiply something by 10, you'll get a 0 at the end. Besides, infinite is quite debatable. You can't calculate with infinite, same way as you can't calculate with 0.
^^^^however LA-384 when infinite is viewed as a theory then it is still able to be calculated, as with imaginary numbers
Well one way of thinking of infinity is equal continuous adding. Consider .999~ increasing by one digit every second. 1 sec=.9 2 sec =.99 3 sec= .999 4 sec=.9999 Just as time infinitely goes on, the number is infinitely getting closer to 1. In real life, the number would increase much faster. so at the first second x=.9, and 10x = 9.0 10x - x = 8.1 at the second second x=.99 and 10x = 9.90 10x -x = 8.91 at the third second x=.999 and 10x = 9.990 10x - x = 8.991 and so on so at any point in which x=.999~ is increasing, 10x has a zero at the end at every point by being ahead one digit place just as LA-384 pointed out. This is true because a number higher than infinity is infinity+2. At any point infinity is at, infinity + 2 will always be 2 integers higher. Even higher would be infinity +n where n is all real positive numbers.
Think about this x = .55(repeating) 10x = 5.55(repeating) 5.55(repeating)-.55(repeating)= 5 5/5 = 1/1 So its impossible unless you cant multiply by ten for some reason and heres a way to disprove that. 1.596*10=15.96 no zero
this is wrong and right....its ur basic let statement 10x-x=9.999(repeat) (combine like terms) 9x=9.999 (divide) 9x/9=9.999(repeat)/9 x=1.111(repeat) but also if you substitute in .999(repeat) 10(.999(repeat))=9.999(repeat) 9.99(repeat)=9.999 now that answer is 1 so algebraically it is wrong but using real numbers over variables its right i dont have my grade 10 math yet so i may be wrong
ok i posted this on a different forum and this is what i got This whole .999999999 = 1 thing always used to confuse me to death back in the middle schools days, it just didnt make sense. However it is known to ----- mathematicians that .9 repeating does in fact equal 1. This first proof raggher showed is one of many ways to conclude this fact. Raggher, the problem with your answer is that you were not keeping both sides of the equation balanced. you had, x= .99999999 then multiplied by 10 on each side to get 10x = 9.999999 (which is correct) but then when you subracted x from the left side of the equation, you didnt subtract it from the right side as well, which resulted in your incorrect answer. You wrote 10x - x = 9.9999999 (didnt subtract the .999999 from the right like the original proof). so, both of you were on the right track, but you violated one of the laws of mathematics, so the original proof was correct. Another, slightly easier way to prove this is using fractions. 1/3 = .3333333333333 3 * 1/3 = .33333333333 * 3 3/3 = .99999999999999 1 = .999999999…. One can also prove that .9 repeating = 1 by using an infinite geometric series (this is the proof used by ----- mathematicians) I know that .999999999… each 9 in this number is (1/10) smaller than the previous 9 since that is the way a base 10 numerical system works, so the ratio here if we added an infinite amount of numbers to get .99999 would be (1/10) (i.e. .9 + .09 + .009, etc) So I can conclude that this series converges since r (the ratio) is less than 1. to find the infinite sum of this series the equation is (a * r)/ (1 – r) where a = 9 in this case since that is our base number. So our series looks like this (the changing exponents on all the one tenths are there since that is the ratio, each is 1/10 smaller than the previous term) .99999… = 9(1/10)^1 + 9(1/10)^2 + 9(1/10)^3 + …(continues infinitely) = a * r / (1 – r) a * r / (1 – r) = 9*(1/10) / (1 – (1/10)) = (9/10)/(9/10) = 1.
Dudes ppl have posted proof on wikipedia... wikipedia is the biggest group of nerds in history, they probably fought about this issue for days... if wiki says its on, its one. My teacher also taught me that it was one, as xlink has already given the complex explanation the simple one is this 0.999... x10 = 9.9999.... which can be seen as 9 + 0.9999.... -0.9999 =9 You cant fault that equation no matter how hard you tried, many people in my class refused to accept it till they say that..
x = .55(repeating) 10x = 5.55(repeating) 5.55(repeating)-.55(repeating)= 5 5/5 = 1/1 so does .55repeating = 1?
Ha! No. This theory is incorrect. I've seen it many times before and no one seems to agree. Look, If .999 (Repeating) was equal to 1. It would be 1 and not .999 (Repeating). Common Sense saves the day!
In mathematics, the recurring decimal 0.999… , which is also written as 0.\bar{9} , 0.\dot{9} or \ 0.(9), denotes a real number equal to 1. In other words, "0.999…" represents the same number as the symbol "1". The equality has long been accepted by ----- mathematicians and taught in textbooks. Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience. I cant see how you can fight this... Wikipedia is maintained by the collective intelligence of thousands (if not millions) of math nerds LINK to Article. Number systems in which 0.999… is strictly less than 1 can be constructed, but only outside the standard real number system which is used in elementary mathematics. This is the only line in the entire article that suggest you can prove it wrong...but u have to invent a new number system to do so.... Anyways i have decided the 0.999 definitely equals 1.
Well like you just said depends which math system your in.. in lower maths .999= .999 and 1=1 but after looking at the equations i can see how .999=1 in certain maths... higher level maths
