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radscorpion9
Profile Blog Joined March 2011
Canada2252 Posts
Last Edited: 2014-01-06 00:43:42
January 06 2014 00:42 GMT
#441
Its often stated in mathematics that 0.99999... (repeating until infinity) is equal to one. The proof that is commonly used is that we associate 1/3 with 0.3333..., and since 3*(1/3) = 1, it is clear that 0.9999... = 1.

But this proof seems inadequate because we are using what we are trying to prove in the proof itself...that is, it should be just as unacceptable that 1/3 can be written as an infinite 'series' of threes as that a one can be written as an infinite series of nines.

So to rephrase: Is 1/3 = 0.3333... just supposed to be taken as an axiom of mathematics, or is there actually a good reason to believe that an infinite series of threes can actually equal a rational number? I can certainly understand it in terms of limits, perhaps, where as we add additional threes to the decimal expansion it approaches the value of 1/3. But as far as I know there is no such thing as infinity as a real number in math, so the expression 0.333... doesn't really make sense, and so I have a hard time equating it with a real (rational) number.
frogrubdown
Profile Blog Joined June 2011
1266 Posts
January 06 2014 01:07 GMT
#442
On January 06 2014 09:42 radscorpion9 wrote:
Its often stated in mathematics that 0.99999... (repeating until infinity) is equal to one. The proof that is commonly used is that we associate 1/3 with 0.3333..., and since 3*(1/3) = 1, it is clear that 0.9999... = 1.

But this proof seems inadequate because we are using what we are trying to prove in the proof itself...that is, it should be just as unacceptable that 1/3 can be written as an infinite 'series' of threes as that a one can be written as an infinite series of nines.

So to rephrase: Is 1/3 = 0.3333... just supposed to be taken as an axiom of mathematics, or is there actually a good reason to believe that an infinite series of threes can actually equal a rational number? I can certainly understand it in terms of limits, perhaps, where as we add additional threes to the decimal expansion it approaches the value of 1/3. But as far as I know there is no such thing as infinity as a real number in math, so the expression 0.333... doesn't really make sense, and so I have a hard time equating it with a real (rational) number.


Limits don't approach things in math; they equal things. The "approaching" talk (more commonly used for what the argument of a function does in a limit) is a metaphor that only results in confusion.

In particular, the limit of the sequence partial sums (3/10, 3/10+3/100,3/10+3/100+3/1000,...) equals 1/3. 0.3333... is defined as the limit of this sequence of partial sums, so it too equals 1/3.

Of course, if you're going to take this detour through sequence limits, you might as well show that .999... equals one directly using such limits rather than going through 1/3.
Simberto
Profile Blog Joined July 2010
Germany11507 Posts
January 06 2014 01:07 GMT
#443
There is a good reason. The reason is the convergence theorem from geometric series, which has been proven to be true. Look the proof up if you don't believe me in this part.

An infinite decimal number is a geometric series, namely

0.333...= 3/10 + 3/100 + 3/1000 +... = Sumi(1-inf) 3*(1/10)^i

And this series is
= 3/(1-1/10) - 3
= 30/9 - 3
= 1/3
rebdomine
Profile Blog Joined October 2010
6040 Posts
January 06 2014 02:48 GMT
#444
Why is this thread so full of math? Does this imply that math is stupid?
"Just because you are correct doesn't mean you are right!"
Ettick
Profile Blog Joined June 2011
United States2434 Posts
January 06 2014 02:48 GMT
#445
On January 06 2014 11:48 rebdomine wrote:
Why is this thread so full of math? Does this imply that math is stupid?

Yes
[UoN]Sentinel
Profile Blog Joined November 2009
United States11320 Posts
January 06 2014 02:54 GMT
#446
On January 06 2014 11:48 Ettick wrote:
Show nested quote +
On January 06 2014 11:48 rebdomine wrote:
Why is this thread so full of math? Does this imply that math is stupid?

Yes

Day9 is a math major, are you calling Day9 stupid?
Нас зовет дух отцов, память старых бойцов, дух Москвы и твердыня Полтавы
Ettick
Profile Blog Joined June 2011
United States2434 Posts
January 06 2014 02:59 GMT
#447
On January 06 2014 11:54 [UoN]Sentinel wrote:
Show nested quote +
On January 06 2014 11:48 Ettick wrote:
On January 06 2014 11:48 rebdomine wrote:
Why is this thread so full of math? Does this imply that math is stupid?

Yes

Day9 is a math major, are you calling Day9 stupid?

No, smart people can study stupid things and do all the time.
Orcasgt24
Profile Joined August 2011
Canada3238 Posts
January 06 2014 03:19 GMT
#448
I'm gonna order some pizza. Should I get it from Little Caesars, Pizza Hut, Pizza 73, Panago, Boston Pizza or Papa Johns?
In Hearthstone we pray to RNGesus. When Yogg-Saron hits the field, RNGod gets to work
Jormundr
Profile Joined July 2011
United States1678 Posts
January 06 2014 03:23 GMT
#449
On January 06 2014 12:19 Orcasgt24 wrote:
I'm gonna order some pizza. Should I get it from Little Caesars, Pizza Hut, Pizza 73, Panago, Boston Pizza or Papa Johns?

Burger King.
Capitalism is beneficial for people who work harder than other people. Under capitalism the only way to make more money is to work harder then your competitors whether they be other companies or workers. ~ Vegetarian
[UoN]Sentinel
Profile Blog Joined November 2009
United States11320 Posts
January 06 2014 03:28 GMT
#450
Pizza Hut if you don't mind getting your hands oily. I prefer them when I have napkins ready
Нас зовет дух отцов, память старых бойцов, дух Москвы и твердыня Полтавы
rebdomine
Profile Blog Joined October 2010
6040 Posts
January 06 2014 04:32 GMT
#451
On January 06 2014 12:19 Orcasgt24 wrote:
I'm gonna order some pizza. Should I get it from Little Caesars, Pizza Hut, Pizza 73, Panago, Boston Pizza or Papa Johns?


Domino's
"Just because you are correct doesn't mean you are right!"
Danglars
Profile Blog Joined August 2010
United States12133 Posts
January 06 2014 04:40 GMT
#452
Papa John's
They dipped their toe in eSports
Great armies come from happy zealots, and happy zealots come from California!
TL+ Member
Najda
Profile Joined June 2010
United States3765 Posts
January 06 2014 21:20 GMT
#453
On January 06 2014 10:07 Simberto wrote:
There is a good reason. The reason is the convergence theorem from geometric series, which has been proven to be true. Look the proof up if you don't believe me in this part.

An infinite decimal number is a geometric series, namely

0.333...= 3/10 + 3/100 + 3/1000 +... = Sumi(1-inf) 3*(1/10)^i

And this series is
= 3/(1-1/10) - 3
= 30/9 - 3
= 1/3


Also this:

n = .9999999

10n = 9.999999999
10n - n = 9
9n = 9
n = 1

Unrelated, I'm at work with a ton of downtime. Any work-friendly websites that can be entertaining to fill the time?
Dark_Chill
Profile Joined May 2011
Canada3353 Posts
January 06 2014 23:59 GMT
#454
On January 04 2014 05:28 Najda wrote:
Show nested quote +
On January 03 2014 18:54 IAmWithStupid wrote:
So I was watching Day[9]'s story time about graham's number.
+ Show Spoiler +


I also know that π is irrational number, so somewhere in it there is every combination of digits, such as my birthday, yours, bank account of Bill Gates and its pin-code, etc.

So my stupid question is: does the order happens in π after graham's number of written digits or somewhere in π the graham's number is written?
(My opinion is the second option. Am I right?)


Since π continues on for infinity, it therefore will contain graham's number within it at some point.


I don't have the mathematical proof for this, but statistically speaking, isn't that false? Flip a coin an infinite amount of times, and you could still get tails every time (going on to infinity could just mean an infinite amount of tails). Therefore, pi being infinite shouldn't be a sufficient reason for it containing every possible combination.
CUTE MAKES RIGHT
Najda
Profile Joined June 2010
United States3765 Posts
January 07 2014 00:06 GMT
#455
On January 07 2014 08:59 Dark_Chill wrote:
Show nested quote +
On January 04 2014 05:28 Najda wrote:
On January 03 2014 18:54 IAmWithStupid wrote:
So I was watching Day[9]'s story time about graham's number.
+ Show Spoiler +
http://www.youtube.com/watch?v=1N6cOC2P8fQ


I also know that π is irrational number, so somewhere in it there is every combination of digits, such as my birthday, yours, bank account of Bill Gates and its pin-code, etc.

So my stupid question is: does the order happens in π after graham's number of written digits or somewhere in π the graham's number is written?
(My opinion is the second option. Am I right?)


Since π continues on for infinity, it therefore will contain graham's number within it at some point.


I don't have the mathematical proof for this, but statistically speaking, isn't that false? Flip a coin an infinite amount of times, and you could still get tails every time (going on to infinity could just mean an infinite amount of tails). Therefore, pi being infinite shouldn't be a sufficient reason for it containing every possible combination.


I was wrong in saying that, but not for the reason you listed. If the digits of Pi were true random then it would indeed contain all possible combinations of digits, including Graham's number, but I was incorrect in assuming that Pi had that property. It apparently has yet to be proven, but the general thought is that it likely does have that attribute.

In response to your coin problem, I could be wrong in saying this, but I believe if you flipped a coin an infinite amount of times, somewhere within that series would be an infinite number of tails, as it would have every single possible outcome contained within the series.
NewSunshine
Profile Joined July 2011
United States5938 Posts
January 07 2014 00:58 GMT
#456
On January 07 2014 09:06 Najda wrote:
In response to your coin problem, I could be wrong in saying this, but I believe if you flipped a coin an infinite amount of times, somewhere within that series would be an infinite number of tails, as it would have every single possible outcome contained within the series.

Infinity. Filling math with bullshit since the beginning of time. Possibly longer.
"If you find yourself feeling lost, take pride in the accuracy of your feelings." - Night Vale
3FFA
Profile Blog Joined February 2010
United States3931 Posts
Last Edited: 2014-01-07 13:31:23
January 07 2014 13:30 GMT
#457
What is the value of infinity?

How stupid is stupid?

Is R1CH > Liquid'Nazgul?

Why does math exist?

Why does my school block educational sites with the label 'gaming' while leaving this site unblocked even though there is a picture of a gamer on the frontpage almost every day?
"As long as it comes from a pure place and from a honest place, you know, you can write whatever you want."
Najda
Profile Joined June 2010
United States3765 Posts
January 07 2014 13:31 GMT
#458
Infinity doesn't have a value, it's just a concept.
Taekwon
Profile Joined May 2010
United States8155 Posts
January 07 2014 13:39 GMT
#459
Is New York City a foreign country?
▲ ▲ ▲
SnowFantasy
Profile Blog Joined September 2006
4173 Posts
Last Edited: 2014-01-07 13:45:56
January 07 2014 13:40 GMT
#460
On January 07 2014 22:39 Taekwon wrote:
Is New York City a foreign country?

basically.
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