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Cybermonkey

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Registered: 22nd Sep 02
Location: Sydney, Australia
User status: Offline

25th Oct 06 at 11:54

http://upload.wikimedia.org/wikipedia/en/b/b8/999_Perspective.png

Edit - made in to a link so it doesn't skew the page.

[Edited on 25-10-2006 by Ian]

CorsAsh

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Registered: 19th Apr 02
Location: Munich
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25th Oct 06 at 11:56

You're a maniac.

Cybermonkey

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Registered: 22nd Sep 02
Location: Sydney, Australia
User status: Offline

25th Oct 06 at 12:01

Tommy

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Registered: 24th Aug 00
Location: Essex, Colchester
User status: Offline

25th Oct 06 at 12:03

No its not

Cybermonkey

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Registered: 22nd Sep 02
Location: Sydney, Australia
User status: Offline

25th Oct 06 at 12:18

quote:
Originally posted by LoudandLow
No its not

do you really want to argue? really? its a re-occuring decimal exactly equal to 1.

here, have some algebra

Another kind of proof more easily adapts to other repeating decimals. When a number in decimal notation is multiplied by 10, the digits do not change but the decimal separator moves one place to the right. Thus 10 × 0.999… equals 9.999…, which is 9 more than the original number. To see this, consider that subtracting 0.999… from 9.999… can proceed digit by digit; the result is 9 − 9, which is 0, in each of the digits after the decimal separator. But trailing zeros do not change a number, so the difference is exactly 9. The final step uses algebra. Let the decimal number in question, 0.999…, be called c. Then 10c − c = 9. This is the same as 9c = 9. Dividing both sides by 9 completes the proof: c = 1.

c = 0.999…
10c = 9.999…
10c − c = 9.999… − 0.999…
9c = 9
c = 1

The last step — that lim 1/10n = 0 — is often justified by the axiom that the real numbers have the Archimedean property. This limit-based attitude towards 0.999… is often put in more evocative but less precise terms. For example, the 1846 textbook The University Arithmetic explains, ".999 +, continued to infinity = 1, because every annexation of a 9 brings the value closer to 1"; the 1895 Arithmetic for Schools says, "...when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small"

drax

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Registered: 5th Feb 05
Location: Sittingbourne, Kent
User status: Offline

25th Oct 06 at 12:29

But surely... it will never be 1 because there will still be just as many 0.01's recouring between 1 and 0.9~infinate

Ian

Site Administrator

Registered: 28th Aug 99
Location: Liverpool
User status: Online

25th Oct 06 at 12:47

quote:
Originally posted by 1895 Arithmetic for Schools
when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small

But nevertheless present.

ShEp

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Registered: 9th Aug 05
Location: Dingwall, Highland
User status: Offline

25th Oct 06 at 13:35

quote:
Originally posted by Ian

quote:
Originally posted by 1895 Arithmetic for Schools
when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small
But nevertheless present.

Paul_J

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Registered: 6th Jun 02
Location: London
User status: Offline

25th Oct 06 at 13:44

quote:
Originally posted by ShEp

quote:
Originally posted by Ian

quote:
Originally posted by 1895 Arithmetic for Schools
when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small
But nevertheless present.

Tommy

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Registered: 24th Aug 00
Location: Essex, Colchester
User status: Offline

25th Oct 06 at 14:11

How sad u actually bothered explaining it

Cybermonkey

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Registered: 22nd Sep 02
Location: Sydney, Australia
User status: Offline

26th Oct 06 at 09:10

quote:
Originally posted by LoudandLow
How sad u actually bothered explaining it

how sad you actually bothered replying in the first place. YOU SUCK

Steve

Premium Member

Registered: 30th Mar 02
Location: Worcestershire Drives: Defender
User status: Offline

26th Oct 06 at 09:13

page not there?

Cybermonkey

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Registered: 22nd Sep 02
Location: Sydney, Australia
User status: Offline

26th Oct 06 at 11:45

PMSL i might just delete this thread

Hammer

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Registered: 11th Feb 04
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26th Oct 06 at 11:53

Uber geek day

Tommy

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Registered: 24th Aug 00
Location: Essex, Colchester
User status: Offline

26th Oct 06 at 16:10

quote:
Originally posted by Cybermonkey

quote:
Originally posted by LoudandLow
How sad u actually bothered explaining it

how sad you actually bothered replying in the first place. YOU SUCK

Yes i suck off course i do. Am i the geek that is posting as hammer said Uber Geek stuff ?

Im the one that thought ide see how far u would go to prove a point.