Report, edit, etc...Posted by Rantent on 2006-03-01 at 02:18:14
Think about this for a moment.
1/9 = 0.1111111 (the one's continue forever)
2/9 = 0.2222222 (again they repeat forever)
3/9 = 0.3333333 (same thing)
4/9 = 0.4444444 (I hope your getting the point by now)
5/9 = 0.5555556 (rounds up now)
6/9 = 0.6666667
7/9 = 0.7777778
8/9 = 0.8888889
9/9 = 1
Now if you notice the last value is not in fact 1, but a 0.99999 (repeating forever) now this does become 1 when you round any of the 9's in the number.
If this is true, is any number divided by itself truly 1?
Your thoughts.
1/9 = 0.1111111 (the one's continue forever)
2/9 = 0.2222222 (again they repeat forever)
3/9 = 0.3333333 (same thing)
4/9 = 0.4444444 (I hope your getting the point by now)
5/9 = 0.5555556 (rounds up now)
6/9 = 0.6666667
7/9 = 0.7777778
8/9 = 0.8888889
9/9 = 1
Now if you notice the last value is not in fact 1, but a 0.99999 (repeating forever) now this does become 1 when you round any of the 9's in the number.
If this is true, is any number divided by itself truly 1?
Your thoughts.
Report, edit, etc...Posted by DT_Battlekruser on 2006-03-01 at 02:29:32
Why use such lame reasoning? It can be algrebraically proven.
GIVEN: x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
THEREFORE: 0.999... = 1
Q.E.D.
GIVEN: x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
THEREFORE: 0.999... = 1
Q.E.D.
Report, edit, etc...Posted by Lithium on 2006-03-01 at 08:49:54
I've learned this years ago.
10x= 1.11111
- 1x = 0.11111
9x = 1
10x= 1.11111
- 1x = 0.11111
9x = 1
Report, edit, etc...Posted by Kow on 2006-03-01 at 19:14:28
According to your logic, all numbers >= 5/9 (of the 9 denominator) up to nine has that last repeating digit that rounds. .999999 would round the last digit to .999990 but that extra hundred thousanth has to go somewhere, so you get .99990, .9990, .990, .90, 1.
Report, edit, etc...Posted by CheeZe on 2006-03-01 at 20:06:17
No, .9999.... does not equal 1.
8/9 = .8888...
But
9/9 is 1. Not .9999...
DTBK:
That step is wrong. You can't multiply .9999... by 10 unless you want the end to be ..9990. Otherwise, you would end up with an extra ...0009, which is impossible.
Don't try to use silly math tricks like "move one decimal over" or whatever. Use logic.
8/9 = .8888...
But
9/9 is 1. Not .9999...
DTBK:
QUOTE
GIVEN: x = 0.999...
10x = 9.999...
10x = 9.999...
That step is wrong. You can't multiply .9999... by 10 unless you want the end to be ..9990. Otherwise, you would end up with an extra ...0009, which is impossible.
Don't try to use silly math tricks like "move one decimal over" or whatever. Use logic.
Report, edit, etc...Posted by Do-0dan on 2006-03-01 at 20:19:12
QUOTE(DT_Battlekruser @ Mar 1 2006, 01:29 AM)
Why use such lame reasoning? It can be algrebraically proven.
GIVEN: x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
THEREFORE: 0.999... = 1
Q.E.D.
[right][snapback]436925[/snapback][/right]
GIVEN: x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
THEREFORE: 0.999... = 1
Q.E.D.
[right][snapback]436925[/snapback][/right]
you cant just pull numbers/variables out of ur arss, for the 10x - x, you have to minus x on the other side too.....and then it gets all mixed up
if im wrong then plz kill me now for i have not truly understood anything that i have been taught in school
Report, edit, etc...Posted by Mune'R0x on 2006-03-01 at 20:20:18
If I recall, I use to have a signature like this...
1 ˜ .9998 & 1 ? .9998
Take that, Blizzard!
http://www.blizzard.com/press/040401.shtml
QUOTE(Blizzard® Entertainment)
lim(m --> 8) sum(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
1 = 1 & 1 = 10.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
1 ˜ .9998 & 1 ? .9998
Take that, Blizzard!
http://www.blizzard.com/press/040401.shtml
Report, edit, etc...Posted by Kame on 2006-03-01 at 20:20:37
QUOTE(CheeZe @ Mar 1 2006, 06:06 PM)
No, .9999.... does not equal 1.
8/9 = .8888...
But
9/9 is 1. Not .9999...
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8/9 = .8888...
But
9/9 is 1. Not .9999...
[right][snapback]437278[/snapback][/right]
ya. lawl.
Report, edit, etc...Posted by HolySin on 2006-03-01 at 20:23:28
1 = 0.999...
The number continues forever. Since there is no fraction for this number, you cannot add/subtract/divide/multiply this number, so instead, you make life easy and round so it's possible to work with. The 0.999... must be rounded, it really isn't an option.
The number continues forever. Since there is no fraction for this number, you cannot add/subtract/divide/multiply this number, so instead, you make life easy and round so it's possible to work with. The 0.999... must be rounded, it really isn't an option.
Report, edit, etc...Posted by CheeZe on 2006-03-01 at 20:31:31
Rounding .9999... makes it 1. But that doens't make .9999... equal to 1.
Report, edit, etc...Posted by HolySin on 2006-03-01 at 20:34:30
The thing is, you must round to be able to work with it, understand?
Report, edit, etc...Posted by Urmom(U) on 2006-03-01 at 20:46:40
This stuff hurts my head. Wouldn't that mean that I have 1.998 hands?
Report, edit, etc...Posted by Merrell on 2006-03-01 at 20:52:24
It's .999 repeating, as in .99999999999999999 etc. Not .999. You're thinking of a simple fraction, we're talking about an irrational number.
It's really weird.
1/3 = .33¯
2/3 = .66¯
3/3 = 1
(Oh right, thirds are ninths too)
It's really weird.
1/3 = .33¯
2/3 = .66¯
3/3 = 1
(Oh right, thirds are ninths too)
Report, edit, etc...Posted by HolySin on 2006-03-01 at 21:37:17
0.999... = My way of saying 0.9 repeating.
Report, edit, etc...Posted by LegacyWeapon on 2006-03-01 at 21:46:59
QUOTE
Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
Report, edit, etc...Posted by Valug on 2006-03-02 at 08:34:43
[sub]Why are you guys saying 9/9 is .99999? :/[/sub]
Report, edit, etc...Posted by Kyuubi. on 2006-03-02 at 14:12:41
the number .9999 will remain the same if untouched, but it will be equal to 1...only way you'd use the .9999 would be that you want to measure something very precisely...but anyway i guess it depends on what you do to it.
Back in my calculus my prof said something about a=b...probably it relates how .9999=1?
Back in my calculus my prof said something about a=b...probably it relates how .9999=1?
Report, edit, etc...Posted by HolySin on 2006-03-02 at 17:23:14
QUOTE(SlyShadow @ Mar 2 2006, 01:12 PM)
the number .9999 will remain the same if untouched, but it will be equal to 1...only way you'd use the .9999 would be that you want to measure something very precisely...but anyway i guess it depends on what you do to it.
Back in my calculus my prof said something about a=b...probably it relates how .9999=1?
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Back in my calculus my prof said something about a=b...probably it relates how .9999=1?
[right][snapback]437645[/snapback][/right]
Can you be more vague?
Report, edit, etc...Posted by Kyuubi. on 2006-03-02 at 17:33:54
QUOTE(HolySin @ Mar 2 2006, 02:23 PM)
Can you be more vague?
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[right][snapback]437771[/snapback][/right]
uhh if you don't do anything to the .9999 itll stay the same wouldn't it?but rounding it would make it change to a whole number...
for the second part, the prof taught me a very long process,its about a year ago,but he did it how different variables can equal to each other...the a=b using some arithmetic function, i forgot what he did...but i remember he did prove it somehow...just making it how it related to the .9999=1 question...
Report, edit, etc...Posted by Falcon_A on 2006-03-02 at 18:01:10
Am I the only one who thinks this thread is pointless?
Report, edit, etc...Posted by MyStIcAl-MySt on 2006-03-02 at 18:05:19
QUOTE(Falcon_A @ Mar 2 2006, 06:01 PM)
Am I the only one who thinks this thread is pointless?
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[right][snapback]437802[/snapback][/right]
I will agree with you, that this is a silly thread. However everyone has their right to ask a question, somtimes.
Report, edit, etc...Posted by Wilhelm on 2006-03-02 at 18:28:28
9/9 is 1/1, is 1. Just reduce the fraction. 9/9 * 9 = 1/1 = 1
Report, edit, etc...Posted by Falcon_A on 2006-03-02 at 19:07:02
QUOTE
9/9 is 1/1, is 1. Just reduce the fraction. 9/9 * 9 = 1/1 = 1
That's the way I see it.
QUOTE
I will agree with you, that this is a silly thread. However everyone has their right to ask a question, somtimes.
I must agree with that as well.
Report, edit, etc...Posted by DT_Battlekruser on 2006-03-02 at 20:02:02
QUOTE(CheeZe @ Mar 1 2006, 05:06 PM)
Don't try to use silly math tricks like "move one decimal over" or whatever. Use logic.
[right][snapback]437278[/snapback][/right]
[right][snapback]437278[/snapback][/right]
It's not a silly math trick. By definition, 0.999...(10) = 9.999..... It's the foundation of our number system. If you'd like to do it longhand to prove me wrong, I'll see you in infinity years. 0.{9}0 = 0.{9} (where {x} denotes infinite repeating.)
Besdies, LW proved it quite well.
Saying 0.999... ≠ 1 is like saying lim[sub]x→2[/sub] (x[sup]2[/sup]-4)/(x-2) ≠ 4.
Report, edit, etc...Posted by Mini Moose 2707 on 2006-03-02 at 20:08:48
Just because you put .999999999999999999 into your calculator and get 1 doesn't mean they're equal.