booing
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| Joined: 04 May 2009 |
| Total Posts: 6594 |
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| 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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| 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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| 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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| 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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| 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
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| Joined: 17 Nov 2013 |
| Total Posts: 152 |
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| 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
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| Joined: 06 Aug 2010 |
| Total Posts: 9202 |
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| 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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| 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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| 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
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| Joined: 04 May 2009 |
| Total Posts: 6594 |
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| 05 Jun 2014 12:57 PM |
| I disagree with most of these responses. Could you give more proof? |
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| 05 Jun 2014 01:09 PM |
sure
print(1==0.99999999999999999999999999)
true
BAM |
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booing
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| Joined: 04 May 2009 |
| Total Posts: 6594 |
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| 05 Jun 2014 01:09 PM |
| Sigh ugh -_- Thats not proof |
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xSIXx
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| Joined: 06 Aug 2010 |
| Total Posts: 9202 |
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| 05 Jun 2014 01:11 PM |
| islandmaker clearly did not read my post. |
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| 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
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| Joined: 04 May 2009 |
| Total Posts: 6594 |
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| 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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| 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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| 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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| 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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| 05 Jun 2014 01:46 PM |
no it isnt 1 1 - .999999999999999repeated = .11111111111111repeated |
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| 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
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| Joined: 13 Nov 2007 |
| Total Posts: 6315 |
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| 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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| 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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| 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
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| Joined: 06 Jul 2009 |
| Total Posts: 9058 |
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| 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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| 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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