Curse

Senator Tom · Jan 31, 2006, 02:17 AM // 02:17

Quote:

Originally Posted by PieXags

In an exact sense, 0.99999999...(etc) is it's own number (or as close to being defined as a number that it will work for our purposes).

I think every one of us can acknowledge that 0.9999999...(etc) is in fact it's own number, that while insanely close to 1, is not 1. If 0.999999999...(etc) WAS equal to 1, we would never write out 0.9999999...(etc) as it would never have any purpose.

We might as well call it 1, but it's not 1. It's 0.9999999...(etc). I guess the more confusing question is who really cares?

(Obviously...those of us who've posted, I guess.)

yea..i mean it cant be 1 if its .9999...etc...because .99999 is not 1

0.999
1.000

they're different numbers..right?

Quote:

Originally Posted by Shattered Self

x = 0.9999999...(etc.)

10x = 9.99999999...(etc.)

10x-x = 9.999999 - 0.999999
9x = 9
x = 1
0.999999999...(etc.) = 1

omg my brain exploded

unienaule · Jan 31, 2006, 02:33 AM // 02:33

Well, to those who say .9(repeating) is not 1, then what is the difference between 1 and .9(repeating)? As in, 1 - .9(repeating) = ?

dustbunny · Jan 31, 2006, 02:43 AM // 02:43

Shattered Self gave you the mathematical reason why 0.99999... repeated to inifinity is equal to 1. It may or may not be a strange concept that something that comes inifinitely close to 1 is in fact equal to 1. You can't rationalize that it isn't by trying to compare 0.999 to 1.000 (or any number using only a finite number of digits) and it is not an issue of rounding.

Quote:

To conclude alot of math is flawed when you think about it.

for example: pi.

What's wrong with pi? or e, for that matter?

Quote:

So's the square root of the square root of 4.

The square root of the square root of 4 is not the same as the square root of 2.

ahandypeter · Jan 31, 2006, 02:52 AM // 02:52

Quote:

Originally Posted by Paul Mahdi

To conclude alot of math is flawed when you think about it.

for example: pi.

actually, pi is just the circumference of a circle divided by its diameter,

easily and precisely defined, just not number friendly.

and .999 (etc.) = 1

assuming that .999 (etc.) = .9 +.09 +.009 + ... (etc) is an infinite geometric

series with an r of .1 and the first term .9, the sum of such a series would

be .9/(1 - 0.1) which = 1

calamitykell · Jan 31, 2006, 03:02 AM // 03:02

1 / 9 = 0.111111(...)
2 / 9 = 0.222222(...)
3 / 9 = 0.333333(...)
4 / 9 = 0.444444(...)
5 / 9 = 0.555555(...)
6 / 9 = 0.666666(...)
7 / 9 = 0.777777(...)
8 / 9 = 0.888888(...)

10 / 9 = 1.111111(...)
11 / 9 = 1.222222(...)
12 / 9 = 1.333333(...)
etc.

That being said, we have 2 directions in which a pattern is clear. Ascending to 9, and ascending from 9.

Following the pattern from 1-8:

9 / 9 = 0.999999(...)

Following the pattern from 10+:

9 / 9 = 1.000000(...)

There you go. 0.999999(...) = 1.000000(...)

darkMishkin · Jan 31, 2006, 03:04 AM // 03:04

Quote:

Originally Posted by dustbunny

The square root of the square root of 4 is not the same as the square root of 2.

Aha I had forgotten about that! However all I almost right, I said it was an irrational number, whereas it is actually more than one irrational number, +-root(2) and +-root(-2). Right?

lol

Anyway, physics is much much more interesting than maths imo. I might have to tell the story about the black hole corridor (if anyone's interested to know it). I'd have to get out MS Paint for some diagrams though.

calamitykell · Jan 31, 2006, 03:09 AM // 03:09

Quote:

Originally Posted by darkMishkin

Anyway, physics is much much more interesting than maths imo. I might have to tell the story about the black hole corridor (if anyone's interested to know it). I'd have to get out MS Paint for some diagrams though.

Do it. I love physics and math.

TopGun · Jan 31, 2006, 03:14 AM // 03:14

Quote:

Originally Posted by calamitykell

Do it. I love physics and math.

And I love Paint. Do it.

Paul Mahdi · Jan 31, 2006, 03:25 AM // 03:25

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Did I get the point across that pi is a very long number? Now if we can "round" that to 3.14 and still get a circumference that "works" then we can round .9999... to 1 and still get an answer that is satisfactory.

Note: This does not add on to my previous statements
Another Note: I deleted many digits due to size

Murder In China · Jan 31, 2006, 03:26 AM // 03:26

My brain just died....

xxSilhouette · Jan 31, 2006, 05:05 AM // 05:05

and this is why instead of coming home and doing math homework i read forums and play guild wars.

Divinitys Creature · Jan 31, 2006, 05:13 AM // 05:13

0.9999999.... |= 1 IMHO
there is a loss of information in that.
0.999999.... ->1

There was a good debate about this on TGH: http://www.guild-hall.net/forum/show...ighlight=0.999

PieXags · Jan 31, 2006, 05:40 AM // 05:40

Quote:

Originally Posted by calamitykell

1 / 9 = 0.111111(...)
2 / 9 = 0.222222(...)
3 / 9 = 0.333333(...)
4 / 9 = 0.444444(...)
5 / 9 = 0.555555(...)
6 / 9 = 0.666666(...)
7 / 9 = 0.777777(...)
8 / 9 = 0.888888(...)

10 / 9 = 1.111111(...)
11 / 9 = 1.222222(...)
12 / 9 = 1.333333(...)
etc.

That being said, we have 2 directions in which a pattern is clear. Ascending to 9, and ascending from 9.

Following the pattern from 1-8:

9 / 9 = 0.999999(...)

Following the pattern from 10+:

9 / 9 = 1.000000(...)

There you go. 0.999999(...) = 1.000000(...)

...I don't know about you, but 9/9 is one, buddy. 9/9 is not 0.999999(...) Just because it follows a pretty pattern doesn't mean it makes a damn bit of sense.

I suppose the easiest argument to explain how one could consider 0.99999...(etc) to be equal to one is simply with:

1/1 = 1
1/0.999999(...) = 1.00000000000000000000(...)1 (As in, one and then an infinite amount of zeroes with a one at the very "end" that we'll never reach.)

And since 1=1.0000000(...), we can only assume that because of this it's possible for 0.9999999 to equal 1. However this really depends, if you realize that .9999999(...) goes on forever with a shitload of 9's, then it's also safe to say you realize 1.0000000000(...)1 would go on forever (the zeroes of it) until it reaches 1, which we all know we'd never find if in fact the 0's are infinite. So if we never reach the 1 at the very end of 1.0000000000(...)1 that you'd get when 1/0.9999999(...) then we can only assume that in this really stupid sense, 1 = 0.99999(...)

A lot of math is absolutely pointless, however, and you'll never ever acknowledge things like this (or most all the math you were taught) unless you actually become a math teacher, in which case you'll be required to teach the same useless crap to your students.

Mentalmdc · Feb 01, 2006, 05:27 PM // 17:27

What is the difference between 1 and 0.9999999......

0.000000000000000000000000000.......

Fatty Fatty Boomballati · Feb 01, 2006, 10:34 PM // 22:34

Be a rebel and say no it does not.

RPG Matthew · Feb 01, 2006, 10:37 PM // 22:37

my brain has fried just like my old processor chip 2 yrs ago LOL

|Ayron| · Feb 01, 2006, 11:53 PM // 23:53

Quote:

Originally Posted by Shattered Self

x = 0.9999999...(etc.)

10x = 9.99999999...(etc.)

10x-x = 9.999999 - 0.999999
9x = 9
x = 1
0.999999999...(etc.) = 1

Just gonna neaten this up

* means reccuring.

Quote:

F = 0.99999*

10F = 9.99999*

10F - F = 9.99999* - 0.99999* = 9

9F = 9

F = 1 = 0.99999*

It's the best exapmle of failed mathematics according to my old math teacher ("top" guy in mensa or something)

|Ayron| · Feb 01, 2006, 11:56 PM // 23:56

Quote:

Originally Posted by Paul Mahdi

3.
1415926535....

Did you know that mathematicians have gone through over aproxximately a trillion cajillion billion mafillion decimal places of Pi and there is no recuring pattern?

They do use a computer to do this... maybe its missing a pattern since the computer can't be programmed to find something unprogrammable - just a little extra knowledge

Rayndeon · Feb 02, 2006, 03:56 AM // 03:56

I fail to see the point of those who assert that one does not equal zero point nine recurring, in that zero point nine recurring is merely rounded to one. As Shattered Self and |Ayron| have helpfully pointed out using eighth grade mathematics, zero point nine recurring is indeed one. Deductive and inductive reasoning show that this is true. Also, on the subject of pi, it is well defined and yes, it is not user-friendly. For example, here are the first million digits of pi: http://3.141592653589793238462643383...om/index1.html

Last I checked, a site that was only updated in 1995 showed that the University of Tokyo had pi up to 51 billion digits.

Tur713 · Feb 02, 2006, 08:56 AM // 08:56

This thread was refreshingly cerebral just before going to bed. (Math is fun for me) If it hasn't been stated enough 0.999(ect.) does not equal 1, but is most easily and convieniently rounded up to 1.