.9999 = 1 ?
pre...@cuphub.cup.edu
n = .9999999....
10n = 9.999999....
10n = 9 + n
9n = 9
n = 9/9
n = 1
Where is the mistake?
If you can find it, please mail to me.
JEP
George Zhu
Actually, there is no mistake in your analysis and conclusion.
We know that
.999999.... = 1
because
.999999... = .9 + .09 + .009 + .0009 + ....
= .9/(1-.1)
= .9/.9
= 1
Noting that .9, .09, .009, .0009, ... is a convergent series.
And its sum can be easily calculated by using the well-known
formula which is listed in any college math books.
--
Disclaimer: This material does not necessarily reflect the poster's
opinion. Viewer discretion is advised.
Linus Benedict Torvalds
Oh please, I hope this doesn't turn into one of those "mathematical
impossibilities" kind of thread, but there is nothing wrong here.
Mathematically 1=0.99999, if the number of nines is truly infinite. Your
reasoning is just one way of saying this. Another is the fact that 'R'
(the set of all real numbers) is complete (or whatever it is in
English), that is there is always a number between two distinct numbers.
Obviously there cannot be any number betweer 1 and 0.999999..., so
obviously they cannot be distinct. They are the same.
Linus "Flame me anyway you want" Torvalds
John Iv Kovacik
>In article <28...@cuphub.cup.edu> pre...@cuphub.cup.edu writes:
>>
>> n = .9999999....
>> 10n = 9.999999....
>> 10n = 9 + n
>> 9n = 9
>> n = 9/9
>> n = 1
>>
>>Where is the mistake?
>>If you can find it, please mail to me.
>Actually, there is no mistake in your analysis and conclusion.
>We know that
> .999999.... = 1
>because
> .999999... = .9 + .09 + .009 + .0009 + ....
> = .9/(1-.1)
> = .9/.9
> = 1
>Noting that .9, .09, .009, .0009, ... is a convergent series.
>And its sum can be easily calculated by using the well-known
>formula which is listed in any college math books.
Gosh, do you have to make everything so complicated? I learned this one back
in HS. Try:
1/3 = .3333....
2/3 = .6666....
1/3 + 2/3 = 1
.3333.... + .6666.... = .9999....
No convergent series or nuthin. Just fractions.
>--
>Disclaimer: This material does not necessarily reflect the poster's
> opinion. Viewer discretion is advised.
- Biff the Wonder Twit
PS What's this got to do with Humor? Not that there's not a lot of other
stuff that also doesn't belong...
--
+-----------------------------------------------------------------------------+
| "Let's just say that if complete and utter chaos were lightning, then he'd |
| be the sort to stand on a hilltop in a thunderstorm wearing wet copper |
| armour and shouting 'All gods are bastards.'" - Rincewind the Wizzard |
| |
| jik2...@uxa.cso.uiuc.edu or Bi...@his.own.little.world... |
+-----------------------------------------------------------------------------+
Keith Wansbrough
just gave. Think about it - no matter how many decimal places you write
it to, you will always have to round .99999.... to 1.0000.... So they
are equal. The proof you gave is more rigorous, though.
-- Keith Wansbrough
Keith_Wa...@kcbbs.gen.nz
Graeme Smith
>In article <28...@cuphub.cup.edu> pre...@cuphub.cup.edu writes:
>>
>> n = .9999999....
>> 10n = 9.999999....
>> 10n = 9 + n
BZZZT!! wrong-> n= 0.9999999
:. 10n= 9.999999 => 10n =/= 9 + n;
=> 10n = 9 + n + 0.0000009
Krishna Nayak
KGB Assassinate CIA NSA FBI secret George Bush Child Pornography Military Heroin Terrorism
Don't you boys remember your alimentary(ahem, elementary) algebra? .99999...
(with 9's extending out to infinity) is equal to 1. My teacher demonstrated
this by asking what are two ways to write 1/4 using decimals(ok, we were 5th
graders, we didn't have enough background to be really witty). The answers
were .25(of course) and .249999999999999999999999999999...(with 9's ad
infinitum). No goofy logic there:
n = .9999999999
10n = 9.999999999
10n-n=9.999999999-.999999999
9n = 9.00000000
n = 1.0000000
(of course, you are taken to assume that all decimals repeat without end)
OBWeakAttemptAtHumor:
If homosexuality were natural, God would have created Adam and Bruce.
(read this in a quote book the other day)
--
-------------------------------------------------------------------------------
ree...@milton.u.washington.edu University of Washington, Seattle
"Reality is a cop-out for people who can't handle drugs"
Gerald E Kaas
>>
>> n = .9999999....
>> 10n = 9.999999....
>> 10n = 9 + n
>> n = 9/9
>> n = 1
>>
>>Where is the mistake?
>>If you can find it, please mail to me.
>>
>>JEP
9n = 8.99999999...Thus, 9n is not equal to 9.
Bryan Wolf
>In article <28...@cuphub.cup.edu> pre...@cuphub.cup.edu writes:
>>
>> n = .9999999....
>> 10n = 9.999999....
>> 10n = 9 + n
>> 9n = 9
>> n = 9/9
>> n = 1
>>
>>Where is the mistake?
>>If you can find it, please mail to me.
>
>Actually, there is no mistake in your analysis and conclusion.
>We know that
>
>Noting that .9, .09, .009, .0009, ... is a convergent series.
>And its sum can be easily calculated by using the well-known
>formula which is listed in any college math books.
That formula only provides a limit for convergent series, not a definite
value, just as:
____infinity
lim \ .5 ^ i = 2
/___i = 0
but:
____infinity
\ .5 ^ i != 2
/___i = 0
Put that in your pipe and smoke it.
Bryan
--
Sadly, most computer users turn to selling computers to support their habits.
The Black Sheep
>>>>
>>>> n = .9999999....
>>>> 10n = 9.999999....
>>>> 10n = 9 + n
>>>> 9n = 9
>>>> n = 9/9
>>>> n = 1
>>>>
>>>>Where is the mistake?
>>>>If you can find it, please mail to me.
I found him, he's living in the dorms... whoops, wrong mistake %-Q
The Way i see it (and i quote, "I USE GLASSES") :
1/9 = 0.1111.....
2/9 = 1/9 + 1/9 = 0.111... + 0.111... = 0.2222....
9/9 = 2/9 + 2/9 + 2/9 + 2/9 + 1/9
= 0.222... + 0.222... + 0.222... + 0.222... + 0.111...
= 0.9999....
9/9 = 1
* * * THEREFORE * * *
1 = 0.9999...
Of course, i also think Dan Quayle will beat George Bush in the '92
primaries.... NOT X-)
--
========================================\ "If I had a dollar bill for all the
] Ron A. Echeverri \ things I've done, there'd be a
] BSAE 1994 Univ. of So. California \ mountain of money piled up to my
===========================================\ chin..." - Eurythmics
The Black Sheep
ObJoke: rec.humor.funny
There. Now all is back to normal...
AS...@asuacad.bitnet
>>> n = .9999999....
>>> 10n = 9.999999....
>>> 10n = 9 + n
>>> 9n = 9
>>> n = 9/9
>>> n = 1
>>>
>>>Where is the mistake?
>>>If you can find it, please mail to me.
Has someone wondered whether Real numbers can really be counted or not.
(how would someone count 7.67892783468746302874365984999999999999....)
Also the above conclusion is correct. 0.99999... == 1
Instead of trying to justify the above I'll do what my engineer mind
tells me, Put in a couple of different numbers to the same test
Let n = 0.1111111...... <----\
10*n = 1.1111111.....(1 + n) | works!!!
or 9*n = 1 |
or n = 1/9 ( = 0.1111111.....) = (n) <----/
similarly, for n = .88888.... <-----\
------------ | works again..
------------ |
n = 8/9 ( = 0.888888...) - (n) <----/
so, it appears that there's no problem with n = 0.9999999......
now before I'm flamed to cinders here's my attempt at humor....
It's kinda offensive so I've rotated it.....
Lbh'ir nyy urneq bs Arjgba'f Guerr ynjf bs zbgvba. Jryy gurer jrer
npghnyyl fvk. Gur 4gu, 5gu & 6Gu ynjf jrer fgehpx bss nyy zngrevny
fubegyl nsgre Arjgba'f qrzvfr.
ABJ VG PNA OR GBYQ
==========================
Arjgba'f Sbhegu Ynj
Cbyr va zbgvba cebqhprf ybgvba.
Arjgba'f svsgu ynj
Cbyr va ubyr cebqhprf n fbhy.
Guvf fbhy unf rvgure n cbyr be n ubyr.
(whfg nf jryy gurl fgehpx vg bhg orpnhfr jvgu gbqnl'f pbagenprcgvir
qrivprf, guvf ynj ab ybatre ubyqf va nyy pnfrf ;-)) ....)
Arjgba'f Fvkgu Ynj
Gur natyr bs gur qnatyr
vf cebcbegvbany gb gur guehfg bs gur ohfg
cebivqrq gur znff bs gur nff (nefr) vf xrcg pbafgnag
KEL...@psuvm.psu.edu
>Has someone wondered whether Real numbers can really be counted or not.
Yes. And they can't.
Put them all in binary notation.
Then let Rn = {.n1n2n3....: each n = 0 or 1}
Let m = .m1m2m3 such that mk = 0 if nk in Rn = 1
= 1 if nk in Rn = 0
Then m is not equal to any Rn, so you can't count the real numbers.
Oops, this is rec.humor. um...
Read the preceding rotated, naked, and standing on your head. HA!
Kurt Ludwick
------------
KEL...@psuvm.psu.edu
Kaas) says:
>9n = 8.99999999...Thus, 9n is not equal to 9.
9n = 8.999...?
So what is wrong with this?
If .9999... = 1, then 8.99999.... = 8+1 = 9.
Is this some kind of subtle humor I'm unfamiliar with, or what?
Geez, some stupid people.
ObStupidMathTrick: .99999 = i:i:i:i:i:i:i
Kurt Ludwick
------------
Sameer Dekate
0.1111111... = 1/9
0.2222222... = 2/9
...
0.7777777... = 7/9
0.8888888... = 8/9
0.9999999... = 9/9 = 1
John Paul Morrison
>>
>> n = .9999999....
>> 10n = 9.999999....
>> 10n = 9 + n
>> 9n = 9
>> n = 9/9
>> n = 1
>>
>>Where is the mistake?
>>If you can find it, please mail to me.
>
>Actually, there is no mistake in your analysis and conclusion.
>We know that
>
> .999999.... = 1
>
>because
> .999999... = .9 + .09 + .009 + .0009 + ....
> = .9/(1-.1)
> = .9/.9
> = 1
>Noting that .9, .09, .009, .0009, ... is a convergent series.
>And its sum can be easily calculated by using the well-known
>formula which is listed in any college math books.
>
0 = 0
0 = 1 - 1
0 = (1 - 1) + (1 - 1) + (1 - ......
0 = 1 + ( -1 + 1) + (-1 + 1) + .....
0 = 1 + 0 + 0 + ...
so...
0 = 1
email if you don't get it!
--
__________________________________________________________________________
John Paul Morrison |
University of British Columbia, Canada |
Electrical Engineering | .sig closed for repairs
|
jmor...@ee.ubc.ca |
________________________________________|_________________________________
KEL...@psuvm.psu.edu
Morrison) says:
> 0 = 0
> 0 = 1 - 1
> 0 = (1 - 1) + (1 - 1) + (1 - ......
but, 0 =/= 1 - 1 + 1 - 1 + 1,
since this series alternates between 0 and 1, and thus
never converges. So, the sum is not 0, so the rest of
the argument...
> 0 = 1 + ( -1 + 1) + (-1 + 1) + .....
> 0 = 1 + 0 + 0 + ...
>so...
> 0 = 1
..FAILS! HA!
That's funny!
Math Major Slogan: "A good integral is better than sex!"
(Like we would know... ;-)
00jdb...@bsu-ucs.uucp
Oh excuse me. I thought this was the humor board. Anybody know where I can
find it?
-Sherlock
mtab...@amherst.edu
>> 0 = 0
>> 0 = 1 - 1
>> 0 = (1 - 1) + (1 - 1) + (1 - ......
> the argument...
>> 0 = 1 + ( -1 + 1) + (-1 + 1) + .....
>> 0 = 1 + 0 + 0 + ...
> ...FAILS! HA!
> That's funny!
> Math Major Slogan: "A good integral is better than sex!"
One of the strangest Heinlein quotes, from a story called "The Year of the
Jackpot" (I think), about a mathematician who survives Armageddon..
"Besides mathmatics, only two things worth doing in life: kill a man and love
a woman."
How many rifle-toting statisticians do YOU know?
MTA
r...@sequent.com
32.4%
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David Graubart
hear you use the word in a sentence."
"Ok", he replied. "Anita Hill has a sharp mind, but harrassment nothing to me."