Curse

RhanoctJocosa · Jun 05, 2008, 02:03 PM // 14:03

0.999∞ = 1

Prove me wrong

fenix · Jun 05, 2008, 02:04 PM // 14:04

Let x = 0.999∞

1x = 0.999∞
10x = 9.999∞
10x-1x = 9x = 9.999∞ - 0.999∞
9x = 9
x = 1

0.999∞ = 1

PROVE US WRONG

Kattar · Jun 05, 2008, 02:08 PM // 14:08

I'll answer your question with a question.

If one object moves half the distance to the another object, than again and again infinitely, do the two objects ever touch?

t00115577 · Jun 05, 2008, 02:21 PM // 14:21

lol guys, sorry but ye are wrong

let x = .999

1x = .999
10x - 9.990
10x-1x = 9x = 9.990 - .999 = 8.991
8.991 / 9 = .999

therefore .999 = .999

gg

fenix · Jun 05, 2008, 02:22 PM // 14:22

Quote:

Originally Posted by Katsumi

I'll answer your question with a question.

If one object moves half the distance to the another object, than again and again infinitely, do the two objects ever touch?

No, halving to infinity.

But the key is in this line;

10x-1x = 9x = 9.999∞ - 0.999∞

Negates the repeating 9.

t00115577, you fail. It's not .999, it's .999∞

Kattar · Jun 05, 2008, 02:25 PM // 14:25

Quote:

Originally Posted by Fenix

10x-1x = 9x = 9.999∞ - 0.999∞

Negates the repeating 9.

True. Logically, it doesn't seem like it should work.

But it's on teh Wikinets, so it must be true. Lul.

t00115577 · Jun 05, 2008, 02:27 PM // 14:27

cant really multiply by infinity as it doesnt exist, but could look either way at it i guess

fenix · Jun 05, 2008, 02:29 PM // 14:29

Quote:

Originally Posted by Katsumi

True. Logically, it doesn't seem like it should work.

But it's on teh Wikinets, so it must be true. Lul.

Yeah lol, I just saw that on wiki. I had seen this equation years ago, and just remembered it today.

Imagine the uses!

Guildie: "So, what have you been up to today?"
You: "Was farming some ecto in UW"
Guildie: "Oh yeah, how many did you get?"
You: "It was a bad run, I got 0.999∞ ecto"
Guildie: "Uh...what, don't you mean 1?"
You: "0.999∞ = 1!!!"
Guildie has left the game.

(Note, Guildie left the game due to massive mathsplosion in his/her brain)

around · Jun 05, 2008, 02:33 PM // 14:33

They differ by the width of a line.

(ie zero)

Quote:

Originally Posted by Katsumi

I'll answer your question with a question.

If one object moves half the distance to the another object, than again and again infinitely, do the two objects ever touch?

You cannot move infinitely close. What you CAN say is that, as x approaches a value y, f(x) approaches a limit c.

Kattar · Jun 05, 2008, 02:38 PM // 14:38

As far as math goes, it does exist t00115577.

And there's no reason to bring up calculus here, spawn. Well done though, I should have probably remembered that.

*waits for impending mathpolsion*

around · Jun 05, 2008, 02:40 PM // 14:40

ynaut? The question asked is intimately linked to anaylsis. If you consider the function f(x)=0.9(with the 9 repeated x times), as x->infinity (stop laughing), f(x)->1.

Well, 1-f(x) has zero measure, so it is pretty much 0.

Symeon · Jun 05, 2008, 02:45 PM // 14:45

Grab your nearest scientific calculator.

- Type 0.9999999999999999999999 as many 9s as you like. Press [=].

- It should say 0.999999999 (or more 9s if the calculator screen is wider).

- Now press the square root button, then [=]. After one or two presses, you will get 1.

- When you have 1, press [Ans], then [x^2], [=].

- It will say 0.999999999.

If the square root of 1 = 0.999∞, and the square of 0.999∞ = 1, then 0.999∞ must be equal to 1.

around · Jun 05, 2008, 02:46 PM // 14:46

That's not a proof Symeon.

The whole point of 0.9999...... is that it doesn't terminate. Your calculator has just rounded the values, which is to 1. Fenix's proof is probably the best elementary one.

Qwertyfied · Jun 05, 2008, 02:49 PM // 14:49

Sorry, didnt read the thing right - i get what your on about now.

Symeon · Jun 05, 2008, 02:52 PM // 14:52

Quote:

Originally Posted by spawnofebil

That's not a proof Symeon.

The whole point of 0.9999...... is that it doesn't terminate. Your calculator has just rounded the values, which is to 1. Fenix's proof is probably the best elementary one.

I used (0.99999999999999 as many 9s as you like) to represent 0.999∞. If I could type 0.999∞ into a calculator, then [=], it would still say 0.999999999. But I can only type about a hundred 9s into my calculator before it reaches the limit. So if I could type 0.999∞, and it showed 0.999999999, then I pressed the square root button, [=], I would get 1. Then if I pressed [Ans], [x^2], [=], it would show 0.999999999.

Therefore 0.999∞ = 1.