Why .999... is not 1 (April Fool's Joke)

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Howard

Lifer
Oct 14, 1999
47,982
11
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http://www.youtube.com/watch?v=wsOXvQn3JuE&list=UUOGeU-1Fig3rrDjhm9Zs_wg


This video is just a troll/joke (and if you watch it and have half a brain, it's actually kind of funny) by someone who is becoming quite widely known as a mathemusician. (I love Vi's site & videos.) She has another video where she shows that .999... = 1. Since it's not highly technical, I'm moving the thread to OT. -Admin DrPizza
P.S., if you watch the video, pay close attention to the last 2 words - I edited the title to reflect this.
 
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ericloewe

Senior member
Dec 14, 2011
260
0
76
1/3 = 0.3333333333...
1/3 * 3 = 1
0.3333333333... * 3 = 1
0.9999999999... = 1

The real problem is that the decimal system cannot accurately represent 1/3.

Edit: The complicated reasoning used to disprove this proof is crap. 0.999999999... isn't a special number, it's a mis-representation of 1, caused by the use of base 10. Much the same thing happens with base 2 and some common number (I think it was 0.1), which causes floating point representations of 0.1 to be innacurate (much in the same way as 0.9999999... is incorrectly represented in base 10), since FP numbers internally use base 2.
 
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Paul98

Diamond Member
Jan 31, 2010
3,732
199
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LMAO at that epic fail video, can't even do basic math or any understand of proofs.

I like when she starts with .222... = x.
then goes math fail to 2.222... = 2x
she just put a 2 infront of that stuff with no understanding what they were doing before...
should have said 2*.222... = 2x
or 2.222... = 10x

then the final fail, 1/3 = .333....
then you add them together and it doesn't work because you don't add the .000....1 nothing this person said made any sense or did anything to try and disprove .999... = 1

thankfully only an april fools joke.

.999... = 1
 
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Desturel

Senior member
Nov 25, 2001
553
3
81
What ever happened to the old .999... = 1 thread? I remember it being around for about three years in ATOT.
 
Ghiedo27

Ghiedo27

Senior member
Mar 9, 2011
403
0
0
But isn't .3 repeating just an approximation for 1/3? And if so how is that a proof that .9 repeating is anything more than an approximation for 1?
 
M

Mr. Pedantic

Diamond Member
Feb 14, 2010
5,027
0
76
The fact that she sounds so smart, and yet so, so dumb...

I'm hoping she's trolling.
 
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Dude111

Golden Member
Jan 19, 2010
1,497
7
81
Well technically .999 IS NOT 1 -- Its .999 (Just like 1.1 IS NOT 1,its 1.1!!)
 
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Phanuel

Platinum Member
Apr 25, 2008
2,304
2
0
ericloewe said:
You're right. 0.999 != 1.

0.9(9) = 0.999... = 3 * 1/3 = 1
Click to expand...

Well, .9(9repeating) is still not 1. It's still less than 1. This whole thing is so much fail because these people are too high up on their horses to realize that dividing by 3 still means you have, at the end of the day, a .xxxxxxxx4 somewhere because you're truncating. If you're going to say that 1/3+1/3+1/3 = 1. Then sure, that's fine. But the minute you make it a repeating decimal and don't round one of the results to a .xx4, fail.
 
SparkyJJO

SparkyJJO

Lifer
May 16, 2002
13,357
7
81
Phanuel said:
Well, .9(9repeating) is still not 1. It's still less than 1. This whole thing is so much fail because these people are too high up on their horses to realize that dividing by 3 still means you have, at the end of the day, a .xxxxxxxx4 somewhere because you're truncating. If you're going to say that 1/3+1/3+1/3 = 1. Then sure, that's fine. But the minute you make it a repeating decimal and don't round one of the results to a .xx4, fail.
Click to expand...

0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ...

When you're out to millionth billionth zillionth place it no longer matters. A limitation of the decimal system. Deal with it :p
 
H

Howard

Lifer
Oct 14, 1999
47,982
11
81
Phanuel said:
Well, .9(9repeating) is still not 1. It's still less than 1. This whole thing is so much fail because these people are too high up on their horses to realize that dividing by 3 still means you have, at the end of the day, a .xxxxxxxx4 somewhere because you're truncating. If you're going to say that 1/3+1/3+1/3 = 1. Then sure, that's fine. But the minute you make it a repeating decimal and don't round one of the results to a .xx4, fail.
Click to expand...
*head asplodes*
 
P

Phanuel

Platinum Member
Apr 25, 2008
2,304
2
0
SparkyJJO said:
0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ...

When you're out to millionth billionth zillionth place it no longer matters. A limitation of the decimal system. Deal with it :p
Click to expand...

Then write "1/3". Why bother with an endless decimal? Or do .33 .33 and .34?
 
repoman0

repoman0

Diamond Member
Jun 17, 2010
5,191
4,573
136
http://en.wikipedia.org/wiki/Geometric_series

sum over an infinite geometric series with ratio of 1/10 (another way of writing 1/10 + 1/100 + 1/1000 ....... = 0.111........) and you can prove that you get 1/9. multiply by 9 and you prove in the same way that 9/10 + 9/100 + 9/1000 = .999....... = 1, you know, with real math that you can prove with logic and stuff

/thread

disclaimer: didn't watch the video, maybe a troll. Also I guess it'd be more correct to say that the limit is 1, not that it is 1
 
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ericloewe

Senior member
Dec 14, 2011
260
0
76
Phanuel said:
Well, .9(9repeating) is still not 1. It's still less than 1. This whole thing is so much fail because these people are too high up on their horses to realize that dividing by 3 still means you have, at the end of the day, a .xxxxxxxx4 somewhere because you're truncating. If you're going to say that 1/3+1/3+1/3 = 1. Then sure, that's fine. But the minute you make it a repeating decimal and don't round one of the results to a .xx4, fail.
Click to expand...

As has been extensively proven, 0.9(9) = 1

You seem to be unaware of how truncating/rounding a number changes it.

Let's say I want to round 1/3:

0.333 (3333333333333333333333333333...)

3 < 5, so the three stays a three.

Let's truncate it:

0.333 (3333333333333333333333333333...)

because you just throw away everything past 0.333.

Let's try truncating and rounding pi:

3.14159265

Truncated: 3.141
Rounded: 3.142

or

Truncated: 3.14
Rounded: 3.14

See how these operations work?

This alone disproves your theory. If you manage to prove that 1 != 0.9(9) (protip: you won't.), you'll be famous.
 
M

Mark R

Diamond Member
Oct 9, 1999
8,513
16
81
Ghiedo27 said:
But isn't .3 repeating just an approximation for 1/3? And if so how is that a proof that .9 repeating is anything more than an approximation for 1?
Click to expand...

No. 0.3 (recurring) is an exact representation of 1/3. The problem is that it is an inconvenient representation, as it cannot be written in full, it requires that an infinite series is implied.

There's nothing wrong with infinite series; they are important mathematical tools. Pi is the result of an infinite series, as are a number of fundamental mathematical constants.

If you want to write it without specifying that the number recurs (i.e. in a finite number of digits) then this can only be done by approximating. So, this type of representation is a bit inconvenient.

However, recurring sequences occur in other number systems.

E.g. If you take the number 1/10, or 0.1 and you convert it into binary you get 0.000110011001100(1100 recurring). This recurring number is an exact representation of 0.1, but any practical method of writing it in a finite number of digits will lead to an approximation.
 
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Fayd

Fayd

Diamond Member
Jun 28, 2001
7,970
2
76
www.manwhoring.com
Phanuel said:
Well, .9(9repeating) is still not 1. It's still less than 1. This whole thing is so much fail because these people are too high up on their horses to realize that dividing by 3 still means you have, at the end of the day, a .xxxxxxxx4 somewhere because you're truncating. If you're going to say that 1/3+1/3+1/3 = 1. Then sure, that's fine. But the minute you make it a repeating decimal and don't round one of the results to a .xx4, fail.
Click to expand...

but you're not truncating. that's the point of a repeating decimal.
 
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