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0.999... = 1

Hey everyone :biggrin:

, just read something interesting:

0.999... = 1

0.999... = x (1)
9.99... = 10x (2)

(2) - (1)

9 = 9x
x = 1

x= 1, 0.999... = 1 !
-----------------------------------------------------------------------------------------------------------------------

1/3 = 0.333...

Times both sides by 3

1 = 0.999...

Cya!

Reply 1

Dilute

15

Yes....

But what happens when you have 0.999...99^infinity? Is it still 1?

Reply 2

bob_54321

But what happens when you have 0.999...99^infinity? Is it still 1?

i'd have thought that that was 0, hmm, it's clearly not though, so yeah, i guess it's 1.

but yeah, 0.9999 . . . = 1 as far as i know. that's why you have strictly inequality signs, to say less than one, rather than less than or equal to 0.999 . . .

Reply 3

Gaz031

15

Your proof leaves a little to be desired but yes, 0.999... = 1 is correct.

Reply 4

AlphaNumeric

10

Since 0.9r =1, you get the obvious identity (0.9r)^infinity = 1^infinity = 1, though you might want to do it by limits to be rigorous.

There are loads of proofs (at least 10 at last count for me). Many of them are on Wikipedia here : http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

The worst thread I have ever partaken in was arguging with a bunch of utter utter morons that 0.9r IS 1 for over 40 pages!!

Reply 5

Piggy

1

AlphaNumeric

The worst thread I have ever partaken in was arguging with a bunch of utter utter morons that 0.9r IS 1 for over 40 pages!!

Oooh this is interesting! Forgive my ignorance but why is "equals to" different from "is"? Is there some mathematical argument or is it purely grammatical?

Reply 6

Wrangler

2

NO WAY - I hate this! 0.9r is NOT equal to 1!

Aha, take that Mr Maths! :p:

Reply 7

Chewwy

17

Piggy

Oooh this is interesting! Forgive my ignorance but why is "equals to" different from "is"? Is there some mathematical argument or is it purely grammatical?

they're the same, i think he was tryign to say he was arguing they are the same, while he was arguing with people who thought they weren't.

anyway, this thread ends now.

Reply 8

yazan_l

5

chewwy

anyway, this thread ends now.

you r not who started the thread, and not a mod. so u have NOTHING to do with when this thread ends!

Reply 9

Evil Phoenix

2

Jess89

Hey everyone :biggrin:

, just read something interesting:

0.999... = 1

0.999... = x (1)
9.99... = 10x (2)

(2) - (1)

9 = 9x
x = 1

x= 1, 0.999... = 1 !
-----------------------------------------------------------------------------------------------------------------------

1/3 = 0.333...

Times both sides by 3

1 = 0.999...

Cya!

yes, that is a mathematically accepted equality :rolleyes:

Reply 10

The Centipe

10

Wrangler

NO WAY - I hate this! 0.9r is NOT equal to 1!

Aha, take that Mr Maths! :p:

Of course it is.

Reply 11

Gaz031

15

yazan_l

you r not who started the thread, and not a mod. so u have NOTHING to do with when this thread ends!

I think everyone who has seen how nightmarish these 0.999...=1 topics can become knows that it would probably be in the best interests of the mental health of everyone if it were to end.
Then again, next time perhaps all those 'in the know' could stand back and watch the carnage.

Reply 12

yusufu

16

yazan_l

you r not who started the thread, and not a mod. so u have NOTHING to do with when this thread ends!

long live this thread! :biggrin:

Reply 13

yazan_l

5

Gaz031

I think everyone who has seen how nightmarish these 0.999...=1 topics can become knows that it would probably be in the best interests of the mental health of everyone if it were to end.
Then again, next time perhaps all those 'in the know' could stand back and watch the carnage.

i totally agree... but it doesnt mean that chewwy has the right to decide when this thread ends!
i totally agree that this will take us to an infinite pages of talking... but it's everyone's right to know why 0.999... = 1

Reply 14

screenager

2

I'm almost certain I read a thread that was exactly the same as this the other day.

Reply 15

anonpls123

OP

Gaz031

Your proof leaves a little to be desired but yes, 0.999... = 1 is correct.

Fine then, post whatever amazing proof you have up ur sleeves, im sorry if mine isnt very good, but it's the first time i've read about this.

Reply 16

yazan_l

5

rewmck

I'm almost certain I read a thread that was exactly the same as this the other day.

ya there are more than one thread!
ending this thread would had been so easy only if someone posted the link of one of those threads...

Reply 17

Chewwy

17

Jess89

Fine then, post whatever amazing proof you have up ur sleeves, im sorry if mine isnt very good, but it's the first time i've read about this.

look at the link in alphanumeric's post.

yazan_l, the thread had been resolved to your liking. so you're contradicting yourself...

Reply 18

Wrangler

2

I say again, 0.9r is NOT the same as 1 - you're all living in some Mathematical dreamworld. :p:

Reply 19

Piggy

1

I agree (although not about the Mathematical dreamworld part..)

0.999... = 1

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