but he asked a mathamatical question!
if you see it philosophical you can never give an answer to any question. and im really sure he didnt meaned this question to be philosophical. and if you understand this question as mathematical there is only one correct answer.
and i never said that that mathematics are the best way to understand the world and i would never do this.
and your argumentation is still wrong. you dont let out numbers like 0.000000111111111111111111111111.
with a INFINIT amount of digits (in your own words) you let out 0.000000000000000... wich is exactly 0. so your mistake to 1 is the number 0, thus we can say you have exactly 1.
there is a difference between "real life" and mathematics. in mathematics infinit things are allowed. our world maybe doesnt allow it. but this is not the question we are dicussing.
0.999... = 1
This is pretty simple:
1/9 = 0.111...
9 * 1/9 = 9 * 0.111... = 0.999...
9 * 1/9 = 9/9 = 1/1 = 1
0.999... = 1
another example:
x1=0.999 for x2 you steal one digit
x2=0.99
and you see x2 is smaller than x1.
no with infinit digits!!!
x3=0.999... for x4 you steal one digit
x4=0.99...
and here some strange things are happening!!! x3=x4!!!
such crazy things are happening when you have infinit things. this is an easier version of hilberts hotel.
here is another example, and very easily proved. 1/3=.33333...
2/3=.66666.... 3/3 should equal .99999... according to the pattern. However, it also =1. So, the conclusion is that .99999 (repeating)=1
please read the first pages before you are doubleposting things over and over again. we heared these proves often enough now.
this topic just has so many posts cause one user doesnt want to understand that it is so easy.
If you believe in infinity, you will believe anything...
you people have never heard of rounding.
Rounding is unnecessary.
.9 repeating = 1 when rounded to any digit and when not rounded at all.