.999999999999...=1

   
.999999999999=1

No.

.999999999999 ≠ 1

On the other hand, 0.9̅ = 1

*yawn*

ITT: 0.(9)=0.999999999999
Only not really.

ITT: TT

Fail.

Quote from: Tausami on March 15, 2011, 08:11:05 PM

Fail.

Almost a quarter (0.238%) of all humanity would agree with you.

My calculator says you're right.

Mind you, in my job 0.5 = 1 (Also, 0.1=1 if we have to show integers on a spreadsheet) so I might not be the best man to speak to.

obvious statement is obvious.

Almost a quarter (0.238%) of all humanity would agree with you.

Saw that coming, but still laff'd

This isn't really the best proof, either.

1. Prove 1/9 = 0.111...   then continue.


Having said that, I quite like this rather logical statement on the matter.

"If 0.999... does NOT equal 1, then please state the number in between."

"If 0.999... does NOT equal 1, then please state the number in between."

I imagine it would be 0.000...1.

Quote from: Mr Pseudonym on March 16, 2011, 01:23:41 AM

Quote from: Tausami on March 15, 2011, 08:11:05 PM

Fail.

Almost a quarter (0.238%) of all humanity would agree with you.

Please provide proof.

lim_x→∞(1 – 10^-x) = 1 = 0.9̅

Quote from: Daz555 on March 16, 2011, 08:11:26 AM

"If 0.999... does NOT equal 1, then please state the number in between."

I imagine it would be 1 - 0.000...1.

Fixed. Kinda.

Quote from: Saddam Hussein on March 16, 2011, 08:18:39 AM

Quote from: Daz555 on March 16, 2011, 08:11:26 AM

"If 0.999... does NOT equal 1, then please state the number in between."

I imagine it would be 1 - 0.000...1.

Fixed. Kinda.

I would still disagree.

Quote from: ﮎingulaЯiτy on March 16, 2011, 08:42:40 AM

Quote from: Saddam Hussein on March 16, 2011, 08:18:39 AM

Quote from: Daz555 on March 16, 2011, 08:11:26 AM

"If 0.999... does NOT equal 1, then please state the number in between."

I imagine it would be 1 - 0.000...1.

Fixed. Kinda.

I would still disagree.

I think the reason you might disagree is the same reason I put 'kinda'.
The pseudomath was off, but I fully acknowledge it as pseudomath.

I imagine it would be 0.000...1.

Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".

Quote from: Saddam Hussein on March 16, 2011, 08:18:39 AM

I imagine it would be 0.000...1.

Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".

Of course you can.   I've seen it many times, and I'm sure plenty of other people here have too.

Quote from: Daz555 on March 16, 2011, 08:11:26 AM

"If 0.999... does NOT equal 1, then please state the number in between."

I imagine it would be 0.000...1.

Ok, you start writing that down for me and come back when you get to the 1.

This would roughly be equivalent to 0.000...1:

lim_x→∞(10^-x)

So:

10^-1 = 0.1
10^-2 = 0.01
10^-3 = 0.001
etc

So, if we solve for our limit, we get 0.

Thus, lim_x→∞(10^-x) = 0. 0.000...1 is a nonsensical number. It is zero.

I guess the main problem is that one ninth is not 0.11111... it's just an approximation.

I guess the main problem is that one ninth is not 0.11111... it's just an approximation.

No. .1 would be an approximation. .11 would be an approximation.  0.11111... is equal to 1/9.

The statement made by the OP is orrect.

I guess the main problem is that one ninth is not 0.11111... it's just an approximation.

Prove to me that .1111...... is not 1/9.

In the field R (or any other such field), for a number not to be equal to another number, it must be less than or equal to that number.
if A=/=B, then either A>B or A<B. There's also a theorem regarding inequalities that gives us as a direct result, A>C>B or A<C<B.
so tell me, what number is between .11111111111................ and 1/9?

Quote from: PizzaPlanet on March 16, 2011, 09:10:45 AM

Quote from: Saddam Hussein on March 16, 2011, 08:18:39 AM

I imagine it would be 0.000...1.

Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".

Of course you can.   I've seen it many times, and I'm sure plenty of other people here have too.

I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0

Quote from: Saddam Hussein on March 16, 2011, 09:37:00 AM

Quote from: PizzaPlanet on March 16, 2011, 09:10:45 AM

Quote from: Saddam Hussein on March 16, 2011, 08:18:39 AM

I imagine it would be 0.000...1.

Which does not exist. You can't have an infinite amount of zeroes and something after that. That's not how infinity "works".

Of course you can.   I've seen it many times, and I'm sure plenty of other people here have too.

I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0

That's right, but my point is that it's all the difference between .999... and 1.  If we accept that .000...1 is equal to 0, then .999... is equal to 1.

I've seen it many times in maths arguments. Unfortunately, that doesn't make it any less incredibly wrong.
You see, infinity doesn't have an end. You can't put a one after the infinite amount of zeroes ends because, welp, it's infinite. The one never comes, the curtain never drops, the game is never concluded. In other words: 1-0.(9)=0.(0)=0

Actually there are contexts where you can do this. There's nothing wrong with the ordering .000...1 as a map from the omega ordinal to {0,1}. The problem is that this isn't a meaningful real number.

That's right, but my point is that it's all the difference between .999... and 1.  If we accept that .000...1 is equal to 0, then .999... is equal to 1.

No. .000...1 is not equal to 0.00...1 is just not a valid representation of a real number. Think about it this way: When I write something like .123 I mean 1/10 + 2/100 + 3/1000. Now, if I have a non-terminating expansion say 3.1415... then this means i have 3 + 1/10 + 4/100 + 1/1000 + 5/10000 which is a convergent series. Now, ask yourself, what series is represented by .000...1? There isn't any.

If you are still having trouble with this idea it might help to read an intro real analysis textbook which should make clear what is going on. The construction of reals from the rationals using either Dedekind cuts or Cauchy sequences will both make it clear what is going on.