does 1=0.999... ?

s1eepy · 02-13-2008, 01:43 AM

1/3 = 0.333...
2/3 = 0.666...

3/3 = 0.999...

!Xoible · 02-13-2008, 01:53 AM

bro... that's basic math and rounding issues... i'll tutor you for money if you need

truong321 · 02-13-2008, 01:59 AM

lol

s1eepy · 02-13-2008, 01:59 AM

are you sure?

Neema · 02-13-2008, 02:03 AM

give me 999.99 in $$$ and i'll tutor you too

s1eepy · 02-13-2008, 02:13 AM

Quote:

Originally Posted by mantis

bro... that's basic math and rounding issues... i'll tutor you for money if you need

what are the rounding issues?

!Xoible · 02-13-2008, 02:14 AM

Quote:

Originally Posted by s1eepy

what are the rounding issues?

i can think of one issue: the fact you failed ur algebra classes

RenaultOne · 02-13-2008, 02:20 AM

3/3=1 End of story no rounding.

s1eepy · 02-13-2008, 02:20 AM

i guess i was lucky to still obtain a degree in the sciences while failing algebra...

but anyway.. any math whiz's on the board? i'll let this run for a while to see what you guys got before i put down some proofs.

s1eepy · 02-13-2008, 02:33 AM

and fyi "x..." is a mathematical shorthand representing the infinite geometric series x/10 + x/100 + x/1000, ..., so ie. 1/3 = 0.333... is not rounded, but exact.

Kilockel · 02-13-2008, 02:40 AM

Quote:

Originally Posted by s1eepy

1/3 = 0.333...
2/3 = 0.666...

3/3 = 0.999...

I'm going to spoil the fun...

0.999... denotes a real number equal to 1.

Two real numbers are only considered identical if their difference is equal to 0.

The difference of 1 and 0.999... falls under this rule, hence 0.999... equals 1. In short, the "problem" lies with the concept of infinity. That's how I understand it, at least. Correct me if I'm wrong.

Lets see if I can do the math right!

9/9 = 1

9/9 = 9 x 1/9 = 9 x 0.111... = 0.999...

s1eepy · 02-13-2008, 02:45 AM

sup kilockel.
it was actually your ant thread that made me feel like posting a riddle.

Kilockel · 02-13-2008, 02:48 AM

Quote:

Originally Posted by s1eepy

sup kilockel.
it was actually your ant thread that made me feel like posting a riddle.

Hey hey! Glad I could be some inspiration!

Sorry to spoil the fun so soon... I'm not a fan of people blindly believing things without knowing more about them, though.

On a separate note... Did I explain it correctly?

s1eepy · 02-13-2008, 02:56 AM

yea thats one way.

i guess it'll be more fun if i ask to prove that 0.999... < 1.
hmm..

s1eepy · 02-13-2008, 02:59 AM

where are my tutors?

Kilockel · 02-13-2008, 03:01 AM

Quote:

Originally Posted by s1eepy

yea thats one way.

i guess it'll be more fun if i ask to prove that 0.999... < 1.
hmm..

This seems rather simple, if you throw out the fact that 0.999... = 1.

Unfortunately, I'm pretty sure you're not doing that. I can't explain this!

TurboFan · 02-13-2008, 07:53 AM

Quote:

Originally Posted by s1eepy

i guess i was lucky to still obtain a degree in the sciences while failing algebra...

but anyway.. any math whiz's on the board? i'll let this run for a while to see what you guys got before i put down some proofs.

Close, I'm an engineer.

Your logic falls appart with the rounding of 2/3 to .666 repeating. Proper rounding would be .667, which when added to .333 would equal 1. Carry however many sig figs you like.

TurboFan · 02-13-2008, 07:55 AM

Quote:

Originally Posted by s1eepy

and fyi "x..." is a mathematical shorthand representing the infinite geometric series x/10 + x/100 + x/1000, ..., so ie. 1/3 = 0.333... is not rounded, but exact.

Not quite. First, you didn't use "x..." in the opening equation. Second, you've failed to tie your geometric series to the original question. I'd say you'll end up dividing by zero somewhere along the way.

But, thank you for an intelligent post! It's always nice to have a polite intellectual discussion.

TurboFan · 02-13-2008, 07:57 AM

I see the difference in logic. You're theorists, I'm an engineer. Nothing wrong with either, just a different approach!

Kilockel · 02-13-2008, 11:22 AM

Quote:

Originally Posted by TurboFan

I see the difference in logic. You're theorists, I'm an engineer. Nothing wrong with either, just a different approach!

Well, theorists probably isn't the right descriptor...

Everyone (I'm generalizing) knows:

1/3 = 0.333... (where "..." represents an infinitely repeating sequence)

That's simple enough, right? Lets multiply it by three!

3 x 0.333... = 0.999...

Well, that makes sense, doesn't it? So how about this?

3/3 = ?

You just did the math, didn't you? Three thirds is equal to 0.999...! How can that possibly be?

Basically it boils down to the concept of an infinite number, and the fact that two numbers are considered identical if (and ONLY if) their difference is equal to zero. Given any positive value, the difference between 1 and 0.999... is less than this value (this can be demonstrated using some complex maths that I'm not interested in posting). Thus the difference is 0 and the numbers are identical.

This is such a trivial anomaly that it's widely accepted that any mathematical procedure ending in 0.999... is considered to be 1. (This last bit is just my interpretation, and quite possibly over-simplified and incorrect. Take it with a grain of salt.)

DesiGUY · 02-13-2008, 01:15 PM

Pure mathematically: 1 != 0.999...

Everywhere: 1 = 0.999... (if you wanted it to be)

Crimson92 · 02-13-2008, 01:19 PM

this forum is odd at times

View Poll Results: does 1=0.999... ?
yes	19	29.69%
no	45	70.31%
Voters: 64. You may not vote on this poll

02-13-2008, 01:43 AM	#1
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	does 1=0.999... ? 1/3 = 0.333... 2/3 = 0.666... 3/3 = 0.999...
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02-13-2008, 01:53 AM	#2
!Xoible Banned 891 Rep 46,010 Posts Drives: .... Join Date: Nov 2006 Location: . iTrader: (4) Garage List 2008 M3 [4.00] 2007 335i [9.00] 2008 528i [8.00] 2006 Infiniti - G35 ... [8.00]	bro... that's basic math and rounding issues... i'll tutor you for money if you need
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02-13-2008, 01:59 AM	#3
truong321 Second Lieutenant 56 Rep 271 Posts Drives: bmw Join Date: Jun 2007 Location: CA iTrader: (0)	lol __________________
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02-13-2008, 01:59 AM	#4
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	are you sure?
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02-13-2008, 02:03 AM	#5
Neema Major General 830 Rep 7,246 Posts Drives: a few BMWs Join Date: Dec 2006 Location: SoCal iTrader: (12)	give me 999.99 in $$$ and i'll tutor you too __________________ LTMW Widebody+1M front bumper+Slek CF Lip\|M3 Hood\|StopTech BBK\|M-Sport Rear Bumper+DD CF Diffuser\|Custom Recaro Seats\|KW V2\|BavX LS3\|M3 Side Skirts+Custom CF Lip\|BBS CHR 19x10.5+BBS Lugs\|LCI Taillights\|RD Sport Anti-Sway Bars\|GIAC S2\|ER Intercooler+CF Shroud+Charge Pipe\|Tial BOV\|Injen Intake\|MS downpipes\|Custom Exhaust\|BMS Oil Catch Can\|M3 DCT wheel+TiD CF Paddles\|BMW CF Trunk Spoiler\|Aluminum Pedals
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02-13-2008, 02:20 AM	#8
RenaultOne First Lieutenant 21 Rep 302 Posts Drives: BMW E90 328i Jet Black Join Date: Mar 2007 Location: LA / University of California, Berkeley. iTrader: (0)	3/3=1 End of story no rounding. __________________
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02-13-2008, 02:33 AM	#10
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	and fyi "x..." is a mathematical shorthand representing the infinite geometric series x/10 + x/100 + x/1000, ..., so ie. 1/3 = 0.333... is not rounded, but exact.
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02-13-2008, 02:45 AM	#12
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	sup kilockel. it was actually your ant thread that made me feel like posting a riddle.
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02-13-2008, 02:56 AM	#14
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	yea thats one way. i guess it'll be more fun if i ask to prove that 0.999... < 1. hmm..
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02-13-2008, 02:59 AM	#15
s1eepy -_- 36 Rep 204 Posts Drives: e92 Join Date: Dec 2007 Location: socal iTrader: (1)	where are my tutors?
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02-13-2008, 07:57 AM	#19
TurboFan Ski bum 331 Rep 6,198 Posts Drives: sideways Join Date: Aug 2007 Location: Knee deep in the pow iTrader: (8)	I see the difference in logic. You're theorists, I'm an engineer. Nothing wrong with either, just a different approach! __________________ 1999 e46 328i Ti Silver / Black[retired] 2007 e90 335xi Jet Black / Black[retired] 2011 e70 X5 35d Vermillion Red / Cinnamon 2011 e92 M3 LeMans / Fox Red extended
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02-13-2008, 01:15 PM	#21
DesiGUY Banned 88 Rep 76 Posts Drives: Crazy Join Date: Apr 2006 Location: Right behind you iTrader: (0) Garage List 06 BMW 330! [0.00] 99 Mitsubishi Eclipse [0.00]	Pure mathematically: 1 != 0.999... Everywhere: 1 = 0.999... (if you wanted it to be)
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