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Re: 0.999999 = 1?

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booing is not online. booing
Joined: 04 May 2009
Total Posts: 6594
04 Jun 2014 10:28 PM
I saw a thread on this earlier but I want to see what you guys think as of right now. I think it was agreed that its truebecause you can prove it with algebra.
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EchoReaper is online. EchoReaper
Joined: 14 Oct 2008
Total Posts: 4323
04 Jun 2014 10:30 PM
For all practical purposes, 0.999999 repeating is equal to 1. However, if you are coming from a philosophical point of view, 0.99999 repeating does not equal one, or else it would be one. It never truly reaches one, because it repeats to infinity, and infinity doesn't end, but in all mathematical calculations, you can safely substitute 1 and still get the correct answer.
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OneTrueGodTheHolyCow is not online. OneTrueGodTheHolyCow
Joined: 24 Oct 2013
Total Posts: 9350
05 Jun 2014 12:51 AM
What people mean by 0.999999 = 1 I think is just what EchoReaper said, you can safely replace 0.99999 with 1 even if you're dealing with the whole universe to a tiny quark.
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18cwatford is not online. 18cwatford
Joined: 08 Oct 2009
Total Posts: 5410
05 Jun 2014 01:01 AM
Proof:

for i = 0, 1, 0.1 do
print(i, i < 1)
end

output:

0 true
0.1 true
0.2 true
0.3 true
0.4 true
0.5 true
0.6 true
0.7 true
0.8 true
0.9 true
1 true

notice the last one

"1 true"

what's less than 1 but also 1? 0.99999...
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EchoReaper is online. EchoReaper
Joined: 14 Oct 2008
Total Posts: 4323
05 Jun 2014 01:27 AM
@18: That's because computers can't handle infinity, so they round up. You're not being cool.
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Ceoh is not online. Ceoh
Joined: 17 Nov 2013
Total Posts: 152
05 Jun 2014 05:28 AM
Of course it equals 1...

I will now prove it:

1/3 = 0.333333333333...

If you multiply both sides by 3 then:

(1/3)*3 = (0.333333...)*3

3/3 = 0.999999....

1 = 0.999999....

They are the same.
Q.E.D.
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xSIXx is not online. xSIXx
Joined: 06 Aug 2010
Total Posts: 9202
05 Jun 2014 11:40 AM
anyone who has taken at least half a year of calculus would understand that 0.9 repeating does equal one, and if they disagreeed their teacher would probably shame them.


however, it doesn't take calculus or much intelligence to understand that this thread is a _complete_ troll and you should stop replying to it before it turns out to be just like the last one of these.
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BlueTaslem is not online. BlueTaslem
Joined: 11 May 2008
Total Posts: 11060
05 Jun 2014 12:12 PM
EchoReaper: It's not a matter of "practicality". It is not a matter of "philosophy". There ARE surreal numbers which are repeated to infinity but are NOT considered equal--don't be naive and talk about math. Math is not straightforward.

0.999... = 1. Period. It's a true statement, provable in a multitude of ways.

A computer demonstration that it limits to 1 is meaningless because computers cannot by definition provide infinite precision. If you attempted to provide infinite precision in this case you would also never be able to show directly that it is equal to one (@18cwatford).

It is NOT a problem with mathematics. It is solely a deficiency of our numeral system not accurately reflecting the nature of numbers.

Vi Hart has an[other] excellent video on this topic with a number of different proofs of varying rigor.
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islandmaker2012 is not online. islandmaker2012
Joined: 07 Nov 2012
Total Posts: 9327
05 Jun 2014 12:20 PM
0.9r is 1, no doubt about it

it cant calculate more numbers, 0+0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999r is 1, it just is..

the repeating nines is trying to reach 1 by adding 0.09,0.009 etc

and it never really reaches, so its infinite

but because its infinite, it is 1
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booing is not online. booing
Joined: 04 May 2009
Total Posts: 6594
05 Jun 2014 12:57 PM
I disagree with most of these responses. Could you give more proof?
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islandmaker2012 is not online. islandmaker2012
Joined: 07 Nov 2012
Total Posts: 9327
05 Jun 2014 01:09 PM
sure

print(1==0.99999999999999999999999999)

true

BAM
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booing is not online. booing
Joined: 04 May 2009
Total Posts: 6594
05 Jun 2014 01:09 PM
Sigh ugh -_- Thats not proof
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xSIXx is not online. xSIXx
Joined: 06 Aug 2010
Total Posts: 9202
05 Jun 2014 01:11 PM
islandmaker clearly did not read my post.
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islandmaker2012 is not online. islandmaker2012
Joined: 07 Nov 2012
Total Posts: 9327
05 Jun 2014 01:13 PM
oh wow..

yeah, troll can go away now, didn't see the post :P

but it does equal 1
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booing is not online. booing
Joined: 04 May 2009
Total Posts: 6594
05 Jun 2014 01:16 PM
But I asked HOW it equals one. All you did was copy and paste a previous reply if I'm not mistaken.
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islandmaker2012 is not online. islandmaker2012
Joined: 07 Nov 2012
Total Posts: 9327
05 Jun 2014 01:18 PM
you ARE mistaken

0.9repeatingINFINTELY is 1


print(1==0.9999999999999999)
false

print(1==0.99999999999999999)
true
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OneTrueGodTheHolyCow is not online. OneTrueGodTheHolyCow
Joined: 24 Oct 2013
Total Posts: 9350
05 Jun 2014 01:23 PM
well 0.999999 can be replaced by 1 in any case and it doesn't make a difference, so does it really matter? do you mean equivalent in use or equivalent as in the exact same bloody thing no difference whatsoever? because 1 clearly isn't the exact same thing as 0.999999
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OneTrueGodTheHolyCow is not online. OneTrueGodTheHolyCow
Joined: 24 Oct 2013
Total Posts: 9350
05 Jun 2014 01:24 PM
and can we please stop using Lua to test this?

google 'floating point number', it isn't perfect at all
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thetommygun is not online. thetommygun
Joined: 21 Mar 2011
Total Posts: 6159
05 Jun 2014 01:46 PM
no it isnt 1
1 - .999999999999999repeated = .11111111111111repeated
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18cwatford is not online. 18cwatford
Joined: 08 Oct 2009
Total Posts: 5410
05 Jun 2014 02:02 PM
Oh my goodness
did people actually take me seriously with the for loop thing?
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suremark is not online. suremark
Joined: 13 Nov 2007
Total Posts: 6315
05 Jun 2014 02:30 PM
We know that 0.999... ~= 1 and 0.999... < 1. Therefore, there is a number 'n' distinct from 0 such that
    0.999... + n = 1.

We can represent 0.999... as an infinite series:
    0.9 + 0.09 + 0.009 + 0.0009 ... = S_1
Now, we can write n this way:
    n = 1 - S_1 = 1 - (0.9 + 0.09 + 0.009 + 0.0009 + ...)
                = (1 - 0.9) - (0.09 + 0.009 + 0.0009 ...)
                = 0.1 - (0.09 + 0.009 + 0.0009 + ...)
                = 0.1 - 0.1 * S_1
Therefore,
        10n = 10(0.1 - 0.1 * S_1)
        10n = 1 - S_1 = n
        10n = n
Which means that 'n' must equal zero, which is a contradiction to the original definition of 'n'. QED

Effectively, were 0.999... a number distinct from 1, the existence of a smallest number greater than zero would be implied-- and this is impossible because the smallest number which exceeds no positive number (zero) is not contained in the set of positive numbers.
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OneTrueGodTheHolyCow is not online. OneTrueGodTheHolyCow
Joined: 24 Oct 2013
Total Posts: 9350
05 Jun 2014 03:00 PM
if 1 = 0.999... then why is 1 1 and 0.999 have 9s In it


gg athiests
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EchoReaper is online. EchoReaper
Joined: 14 Oct 2008
Total Posts: 4323
05 Jun 2014 03:15 PM
"EchoReaper: It's not a matter of "practicality". It is not a matter of "philosophy". There ARE surreal numbers which are repeated to infinity but are NOT considered equal--don't be naive and talk about math. Math is not straightforward.

0.999... = 1. Period. It's a true statement, provable in a multitude of ways.

A computer demonstration that it limits to 1 is meaningless because computers cannot by definition provide infinite precision. If you attempted to provide infinite precision in this case you would also never be able to show directly that it is equal to one (@18cwatford).

It is NOT a problem with mathematics. It is solely a deficiency of our numeral system not accurately reflecting the nature of numbers."

" n = 1 - S_1 = 1 - (0.9 + 0.09 + 0.009 + 0.0009 + ...)
= (1 - 0.9) - (0.09 + 0.009 + 0.0009 ...)
= 0.1 - (0.09 + 0.009 + 0.0009 + ...)
= 0.1 - 0.1 * S_1
Therefore,
10n = 10(0.1 - 0.1 * S_1)
10n = 1 - S_1 = n
10n = n"

You can't ever reach the conclusion that 0.9r = 1, because 0.9 repeats to INFINITY, which in case you haven't realized, doesn't end. Problem solved. 0.9r ~= 1.
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Oysi is not online. Oysi
Joined: 06 Jul 2009
Total Posts: 9058
05 Jun 2014 03:18 PM
"if 1 = 0.999... then why is 1 1 and 0.999 have 9s In it"

if 1 = 2/2... then why is 1 1 and 2/2 have 2s In it

gg holy cows
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OneTrueGodTheHolyCow is not online. OneTrueGodTheHolyCow
Joined: 24 Oct 2013
Total Posts: 9350
05 Jun 2014 04:10 PM
omg I just realised I can say 'gg atheists' and it makes sense

I love this username so much
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