I never read the thread.. Did .9999999999........ end up = 1?

[Babbles]

OMG I thought Blizzard solved this for everybody!

 

[edro]

Originally posted by: shimsham
STFU ALREADY!!!

 

[Bucks]

Originally posted by: booger711
let x = .9999999999...
10x = 9.9999999...
10x - x = 9x
so...
9.9999999... - .999999999..... = 9 = 9x
so x = 1

.99999999... = 1

why not just say .999999999...+.000000...1 = 1

:roll:

 

[jagec]

Originally posted by: Bucks

Originally posted by: booger711
let x = .9999999999...
10x = 9.9999999...
10x - x = 9x
so...
9.9999999... - .999999999..... = 9 = 9x
so x = 1

.99999999... = 1

why not just say .999999999...+.000000...1 = 1

:roll:

because .00000000......1 = 0 :roll:

 

[vood0g]

Originally posted by: silverpig

Originally posted by: Stunt

Originally posted by: Howard
http://mathforum.org/dr.math/faq/faq.0.9999.html

Please, let's stop arguing.

Again.
The guy took the limit which is not exact as well.

But the 10x thing is sketch as there are different sizes of infinity.

Sure it is. The limit is the exact result. You can approach a limit in a series (which is NOT what is happening here). Jeez I don't know why this is so hard to understand.

lim (n -> inf) Sum (n = 1..inf) 9*(1/10^n) = 1 right?

The series approaches a limit. That limit is EXACTLY 1. Sure the series never makes it there in a finite amount of terms, but this is NOT what 0.999... is. 0.999... is the LIMIT of the above series with an infinite terms.

0.999... does not approach the limit (it's a number, it can't approach anything), it IS the limit, and that limit is exactly 1.

Can you say 2 approaches 3? What is the limit of 2 as n -> infinity? Numbers are numbers.

huh?

 

[mchammer187]

Originally posted by: Babbles
OMG I thought Blizzard solved this for everybody!

 

[shuan24]

so does 1 + 0.0000....1 = 1?

 

[thecrecarc]

.... i am so confusied....... i

 

[mwtgg]

/sigh

 

[DanRydell]

If you haven't taken calculus you should not be allowed to post in this thread. BTW the answer is yes.

 

[DrPizza]

Originally posted by: Stunt
OK...there are two ways to look at it.
for something that goes on forever and is infinitely large...it is effectively 1=0.999...
for all intents and purposes the statement is true.

BUT. there are different degrees of infinity. some inifinties are larger than others. ie. infinity^infinity >> infinity.
multiplying by ten makes an extremely minor adjustment to the size of the infinity.
so it is kind of funky.

Actually, muliplying by 10 doesn't increase the size of infinity, since a 1 to 1 mapping still exists.


Or, to fry your brain a little more... the size of infinity of the counting numbers is the SAME as the size of infinity of positive even numbers. Because there is a direct mapping from one set to the other set.

for every counting number, there is an even number (twice the counting number)
and, for every even number, there is one counting number (1/2 the number)

so... multiplying by 10 doesn't matter.

 

[DrPizza]

Originally posted by: Stunt
...it's highly theoretical and very pointless

Nah, not "highly" to some of us...
Just "highly theoretical" to those who are easily challenged by math.

 

[IAteYourMother]

Sheesh. Just think of it this way: 1/3=.3333333333333333 infinitely. But .33333333333333333 infinitely *3 =.99999999999999999999 infintely. But 1/3 * 3 = 1. Therefore 1= .9999999999999999999 infintely. This is simplified, but is just a better way to help you understand.

 

[puffpio]

Originally posted by: IAteYourMother
Sheesh. Just think of it this way: 1/3=.3333333333333333 infinitely. But .33333333333333333 infinitely *3 =.99999999999999999999 infintely. But 1/3 * 3 = 1. Therefore 1= .9999999999999999999 infintely. This is simplified, but is just a better way to help you understand.

*Shocked at simple and easy to understand explanation!!!