/sci/ - Science & Math

>>14789480
1 exists, 0.9999...8 doesn't

0.9999....9 is not a well defined term and thus is not a real number and cannot be equal to 1. Same issue with 0.999....8

0.999.... is well defined and equal to 1

>>14789480
It's 0.999... not 0.999...9
There's nothing after the ...
The ... is the part that means "take the preceding digits and repeat infinitely."

>>14789480
>>14789491
Haha no :)

1/9 = 0,11111111.... = 1/10 + 1/100 + 1/1000 + ....

Here comes the magic :
18.(1/9) = 18* (1/10 + 1/100 + 1/1000 + ....) = 1,8 + 0,18 + 0,018 + ... = 1,999....98

Let's rebuild our number :
0,999999......98 = 18.(1/9) - 1

Obviously 18/9 olso equals to 2, then checkmate :
0,99999...998 = 2 - 1 = 1

Lel :)

>>14789480
Because [eqn]0.9\bar{9} = 9\sum_{n=1}^{\infty}10^{-n}[/eqn]
which converges to 1

>>14789480
>0.9999...9 is not equal to 0.9999...8?
it's equal
anything after '...' is n*10^-inf=0
so anything after the dots can be ignored

>>14789684
>anything after the dots can be ignored
Like "= 1"

>>14789703

>>14789480
The repeating symbol indicates a stand-in for the next rational number.

.555... means 5/9 in base 10 or any equivalent fraction just as much as .999... means 9/9 or 1.

>>14789717
It's just so fucking stupid subject to talk about
Even a child can see that 1/3 is not equal to 0.333...

>>14789730
>.555... means 5/9
No proof ?


Here is one :

1/9 = 0,1111111111...1 = 1/10 + 1/100 + 1/100 +.....
Then :
9.(1/9) = 0,9999999...9


14/9 = 14.(1/10 + 1/100 + 1/100 +.....) = 1,555555...4

5/9 = 0,5555...5

5/9 = 14/9 - 9/9 = 1,555555...4 - 0,9999999...9 = 0,55555...5

>>14789741
>>14789717
grow up

>>14789782
>grows

>>14789480
because 0.999...9 exists

>>14789480
>why is 0.99999...9 equal to 1
To understand this, you've got to realize that there are multiple ways to evaluate an expression:

#1: Evaluation By Calculation. In this case, you reduce the expression to a single number by calculating all of its operators to obtain a final end result. For example, 2+2 evaluates to 4; and 1 trivially evaluates to 1. However, if you use this method on the infinite series 9/10+9/100+9/1000+..., you will get an undefined result, because the series has no end, and obviously you can't obtain the end result of an endless series of calculations.

#2: Since method #1 obtains an undefined result on an infinite series, they developed a second method of evaluation: Evaluation By Convergence. The infinite series 9/10+9/100+9/1000+... converges to 1, so the series is considered to evaluate to 1 using Evaluation By Convergence.

To evaluate an expression, first try Evaluation By Calculation. If you get an undefined result, then try Evaluation By Convergence. If THAT method yields an undefined result, then try Evaluation By Analytic Continuation. (Evaluation By Analytic Continuation is the method used to show that the series 1-1+1-1+1-... evaluates to 1/2. It also controversially shows that 1+2+3+4+... evaluates to -1/12, and the bizarre nature of that result is why some mathematicians reject this method.) Basically, to evaluate an expression, use the first method that yields a defined result.

The expression "1 = 9/10+9/100+9/1000+..." is interesting because the two sides of the equation use two different methods of evaluation to reduce their respective sides down to 1. Once both sides of the equation have been evaluated, it reduces down to "1 = 1", which evaluates to true.

>>14789598
>1/9 = 0,11111111.... = 1/10 + 1/100 + 1/1000 + ....
here you correctly write the sequence as infinite
> 1,8 + 0,18 + 0,018 + ...
again you represent it as infinite
>1,999....98
here you incorrectly make the series have a finite end, which it doesn't have. Your number is wrong. It would be an infinite repetition of 9s, which is 1. Thats shown by how 18/9 does equal 2.

>>14789480
>why

>>14789730
>next
>rational number
Lol
Lmao even

>>14789480
Why is this question asked like every week? I mean it's funny to bait people to waste their time answering this, but come on, think of something more original. lol
also think of 1 = 0.9999 + 0.00infinite...1. It should be obvious that 0.00000...1 is the same as 0 since there are infinite number of 0's before 1, meaning 1 is never 'reached.' therefore we now have 1 = .99999...9 + 0, which we can simplify to 1 = .99999...9

it doesn't. we just round it up, because that's easier to deal with

0.999... ..9/9 = 1
ez

>>14789480
Because
1=1/3*3=0,33333…3*3=0,99999…9
How the fuck would that work with 0,999…8

1 = 9/10 + 1/10
= 0.9 + 1/10
= 0.99 + 1/100
= 0.999 + 1/1000
:
= 0.9... + 1/inf
= 0.9... + 0
= 0.9...

>>14791129
>here you incorrectly make the series have a finite end, which it doesn't have.
Nope, its says that 999...8 its at infinite, you never reach the "8"because :

0,18 + 0,018 + 0,0018... is always .....999998 at infinite.

That means also with :
>>14789598
That 0,99999...9 equals 0,999999...8 at infinite.(the last "8" and the last "9" are never reach)

>>14791638
>you never reach the "8"
Why not? you have 8 at the end of it every step, no matter how many steps you go

>>14789776
>0,1111111111...1
What the fuck does this mean
There's no final 1 you PIGFUCK

>>14789837
Now you need to start paying rent and get dental insurance

>>14789480
It is, all the way down to zero, which means that every number equals to zero, since we can just round it up

>>14791817
Yes there is?
There's an infinite variation of numbers in there, whether it's 0.11111 or 0.111111111111 or 0.11111111111111111111111111111 or 0.111111111111111111111111111111111111111111111111111111111111

>>14791875
Then it shoudl be
0,1111111111...1 = 1/10 + 1/100 + 1/100 +.....1/10000....0
so how big that last denominator?

>>14789598
>>14789776
>>14791638
>retarded g*rm*n does not understand basic math
>retarded g*rm*n makes post on 4cheddit
>many such cases

>>14791659
And why should it be true for the limit? You can add infinitely many continuous sine waves and make discontinuous function, this is the same shit.
There is no "...8" because that number is simply 1. If a and b are closer than any non-zero distance, they're equal.