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psi
TOAST N' JAM


Registered: 09/05/99
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Diploid]
#22049356 - 08/05/15 06:45 PM (8 years, 5 months ago) |
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Quote:
Diploid said: it seems like it's pretty straightforward to demonstrate by long division that there is no way for the series of repeated digits to end
I didn't exactly follow your orginal question, but I think I get the gist of what you're asking. Read this thread in the Science & Technology forum where a similar question came up. Here's some of the chilli from that thread. See if it helps:
Quote:
Prove: .999 is equal to *EXACTLY* 1
First, two stipulations:
1) We can agree by elementary arithmetic that: 1/3 = .333
2) We can also agree that: .333 + .333 + .333 = .999
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Start by substituting 1/3 for .333 in #2 above yields:
1/3 + 1/3 + 1/3 = .999
Simplify the left gives:
1 = .999
We just showed that (1/3 + 1/3 + 1/3) is equal to .999 and we ALSO showed that 1 is equal equal to .999. Therefore it follows that:
.999 is equal to 1
That is a closely related topic but I'm familiar with that line of argument and it makes sense to me. When I said "it seems like it's pretty straightforward to demonstrate by long division that there is no way for the series of repeated digits to end", that was in reference to me saying that the digits of the decimal representation of 1/7 repeated infinitely, and OP getting all philosophical about infinity in response. Then I posted this image, showing that in calculating 1/7 by long division, you more or less arrive back at your starting point so it's inevitable you'll produce the same sequence of digits again and again (whether we choose to use the term "infinite" or not).

The problem I'm kind of stumbling on is explaining why this pattern seems to hold true: 1 / 9 = 0.1 1 / 99 = 0.01 1 / 999 = 0.001 1 / 9999 = 0.0001 1 / 99999 = 0.00001 1 / 999999 = 0.000001
etc.
Looking at it now I think I'm getting it though.
1 / 99 = 0.01 11 / 99 = 11 (0.01) = 0.11 = 1 / 9
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HatingMeIsEasier
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi] 1
#22049374 - 08/05/15 06:48 PM (8 years, 5 months ago) |
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I already solved why .999 = 1.
The very fraction 1/10 explains everything.
The 1, in itself, is also, coexistently, creating a 9 by forming a space between 9 and itself.
The entire scientific community couldn't figure this out, and I figured it out in 5 minutes - why did I become this intelligent in this world.
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psi
TOAST N' JAM


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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: HatingMeIsEasier]
#22049555 - 08/05/15 07:12 PM (8 years, 5 months ago) |
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Code:
1 ~ 11 11 111 3 • 37 1111 11 • 101 11111 41 • 271 111111 3 • 7 • 11 • 13 • 37 1111111 239 • 4649 11111111 11 • 73 • 101 • 137 111111111 3 • 3 • 37 • 333667 1111111111 11 • 41 • 271 • 9091 11111111111 21649 • 513239 111111111111 3 • 7 • 11 • 13 • 37 • 101 • 9901
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Psychonautica
Cuddly Wuddly Fuccboi


Registered: 04/20/15
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi] 2
#22049559 - 08/05/15 07:12 PM (8 years, 5 months ago) |
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But can you explain why kids love the taste of cinnamon toast crunch?
-------------------- The chances of you even being born, Were forty million to one. There's two parts of the statistic And I want you to live through one 3/8/95 - 7/10/15 Rest In Paradise, Brother. Sheekle said: yeah, i said i was afraid of psychonautica

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psi
TOAST N' JAM


Registered: 09/05/99
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Psychonautica]
#22049562 - 08/05/15 07:13 PM (8 years, 5 months ago) |
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I'm going to say it's the cinnamon. And the sugar.
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HatingMeIsEasier
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi] 1
#22049686 - 08/05/15 07:32 PM (8 years, 5 months ago) |
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Is there any way for you to create an algorithm out of those numbers?
I can see the potential in your formula. It can create an algorithm.
Focus on the 37 - it seems to have a very powerful resonance with 1's.
I will see later if I can turn this into an actual algorithm.
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psi
TOAST N' JAM


Registered: 09/05/99
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi]
#22049846 - 08/05/15 07:58 PM (8 years, 5 months ago) |
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Here's a related series:
Code:
1 ~ 11 11 101 101 1001 7 • 11 • 13 10001 73 • 137 100001 11 • 9091 1000001 101 • 9901 10000001 11 • 909091 100000001 17 • 5882353 1000000001 7 • 11 • 13 • 19 • 52579 10000000001 101 • 3541 • 27961 100000000001 11 • 11 • 23 • 4093 • 8779
These can be combined with the ones from the first table I posted to find bigger numbers of just 1s for which you already know the prime factorization. E.g. 100000000001 * 11111111111 = 1111111111111111111111.
I'm just pulling these numbers from websites with prime factorization calculators. Most of them have restrictions on really big numbers, it seems to be very computationally intensive. I believe the "Sieve of Eratosthenes" is an algorithmic approach relating to prime numbers that some of these sites are using, but I'm not sure of the exact details.
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Diploid
Cuban



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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi] 1
#22049988 - 08/05/15 08:24 PM (8 years, 5 months ago) |
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Here's a related series:
If you like this math geek stuff, you might like reading this entry from my journal about a mathematician named Georg Cantor who rocked the world when he gave the first proof of a mind-blowing notion. He proved that there exists more than one infinity and some are bigger than others.
-------------------- Republican Values: 1) You can't get married to your spouse who is the same sex as you. 2) You can't have an abortion no matter how much you don't want a child. 3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer. 4) We need a smaller, less-intrusive government.
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psi
TOAST N' JAM


Registered: 09/05/99
Posts: 31,456
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Diploid]
#22050185 - 08/05/15 08:57 PM (8 years, 5 months ago) |
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I took a "Mathematical Reasoning for Computer Science" course that touched on that countably/uncountably finite stuff near the end of the course but I'm not really strong on the topic. One thing I found pretty counterintuitive was that the set of rationals is considered to be the same "size" as the set of integers or the set of naturals, even though there are an infinite number of them between any two numbers as with the real numbers. There was a question on a problem set where you had to come up with a program that mapped the rationals to the naturals more or less. I forget the exact details but more or less the sequence followed this kind of pattern:
0/1 (sum of numerator and denominator is 1) 1/1 (sum of numerator and denominator is 2) 1/2 (sum of numerator and denominator is 3) 2/1 (sum of numerator and denominator is 3) ... 1/6 (sum of numerator and denominator is 7) 2/5 " 3/4 " 4/3 " 5/2 " 6/1 " 1/7 (sum of numerator and denominator is 8) 2/6 " 3/5 " 4/4 " 5/3 " 6/2 " 7/1 " etc.
To include the negative rationals you just follow each number by its negative, and anything not in lowest terms (e.g. 2/6) you just skip since it's been covered earlier.
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psi
TOAST N' JAM


Registered: 09/05/99
Posts: 31,456
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Diploid]
#22050262 - 08/05/15 09:09 PM (8 years, 5 months ago) |
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Quote:
A question that then comes up is, is there a Cardinality between Aleph Zero and Aleph One, like an Aleph 0.5? This is a very interesting question. Cantor conjectured that there is no set whose Cardinality is between Aleph Zero and Aleph One. It's called the Continuum Hypothesis. Unfortunately, another clever guy named Kurt Godel showed that this is a formally undecidable question. It can neither be proved true or false even though is it either true or false. It is not possible to know the answer.
The theorem is called Godel Incompleteness. Look it up. It's every bit as weird and beautiful as Cantor's result. I'll write a thread about it some day when I have the energy.
This is cool, I'd heard of Godel's stuff from that book "Godel Escher Bach" but I wasn't aware of the implications about cardinality.
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Psychonautica
Cuddly Wuddly Fuccboi


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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi]
#22050264 - 08/05/15 09:09 PM (8 years, 5 months ago) |
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But can you smell what the rock is cooking?
-------------------- The chances of you even being born, Were forty million to one. There's two parts of the statistic And I want you to live through one 3/8/95 - 7/10/15 Rest In Paradise, Brother. Sheekle said: yeah, i said i was afraid of psychonautica

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Diploid
Cuban



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Posts: 19,274
Loc: Rabbit Hole
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi]
#22050372 - 08/05/15 09:27 PM (8 years, 5 months ago) |
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This is cool, I'd heard of Godel's stuff from that book "Godel Escher Bach" but I wasn't aware of the implications about cardinality.
Hahahaa! Math is delicious sometimes, eh?
I also wrote in my journal about Kurt Godel's Incompleteness. Clicky
-------------------- Republican Values: 1) You can't get married to your spouse who is the same sex as you. 2) You can't have an abortion no matter how much you don't want a child. 3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer. 4) We need a smaller, less-intrusive government.
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TheMule73
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Diploid]
#22050495 - 08/05/15 09:48 PM (8 years, 5 months ago) |
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Quote:
Diploid said: Here's a related series:
If you like this math geek stuff, you might like reading this entry from my journal about a mathematician named Georg Cantor who rocked the world when he gave the first proof of a mind-blowing notion. He proved that there exists more than one infinity and some are bigger than others. 
I'm gonna have to agree with Wittgenstein that it isn't that there are different sizes of infinities, but different kinds
Nonetheless I love Cantor's work. His theological-defense of his transfinite numbers is pretty cool
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TheMule73
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi]
#22050519 - 08/05/15 09:54 PM (8 years, 5 months ago) |
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Quote:
psi said:
Quote:
A question that then comes up is, is there a Cardinality between Aleph Zero and Aleph One, like an Aleph 0.5? This is a very interesting question. Cantor conjectured that there is no set whose Cardinality is between Aleph Zero and Aleph One. It's called the Continuum Hypothesis. Unfortunately, another clever guy named Kurt Godel showed that this is a formally undecidable question. It can neither be proved true or false even though is it either true or false. It is not possible to know the answer.
The theorem is called Godel Incompleteness. Look it up. It's every bit as weird and beautiful as Cantor's result. I'll write a thread about it some day when I have the energy.
This is cool, I'd heard of Godel's stuff from that book "Godel Escher Bach" but I wasn't aware of the implications about cardinality.
I thought Godel proved that any axiomatic system--strong enough to do peano arithemetic--will never be complete enough to prove certain statements. That is, that one would always need to appeal to a new axiom to prove some statement. But then when this new axiom arises, another different proposition would still be there that would only be proven through the addition of another new axiom.
The continuum hypothesis has not been proven unprovable. It's been proven that it cannot be proven using the axioms of ZF. Another guy then came along and showed hat the continuum hypothesis cannot be disproven using these same axioms as well.
As for undecidable propositions, the following link is a pretty good summary of Wittgenstein's mathematical thoughts. Very thought-provoking, and a good chunk deals with undecidable propositions.
http://plato.stanford.edu/entries/wittgenstein-mathematics/
Also, it's interesting to note that Godel was part of the Vienna Circle which intensely studied Wittgenstein's Tractatus in the years after it's debut.
Edited by TheMule73 (08/05/15 10:14 PM)
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HatingMeIsEasier
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: psi]
#22051048 - 08/05/15 11:34 PM (8 years, 5 months ago) |
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Alright.
I made a video that fully puts ".999 = 1" into quantum action:
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Prisoner#1
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: HatingMeIsEasier]
#22051223 - 08/06/15 12:17 AM (8 years, 5 months ago) |
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Quote:
HatingMeIsEasier said: Are you blind? Or are you just in denial?
1 1+1+2=4 1+1+2+4+3=11 <--- 1+1 = 2 1+1+2+4+3+11+4=26 <--- 2+6 = 8 1+1+2+4+3+11+4+26+5=57
Yeah, you're blind.
You cannot see it, even when it is in front of your face.
how about explaining it
first explain why you add the double digit numbers together except in the last like where 57 remains, I mean 5+7=12 1+2=3, why didnt you continue, why the sudden leap to no longer following the rules you set. I see this with the numerology conspiracy nutters all the time and you are clearly no different
now, how about an explanation as to the whole, detailed if you would since you cant expect us to read your mind and take from it what all this means unless you want us to know that you can do first grade math problems
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Confucian
...


Registered: 03/31/09
Posts: 1,741
Loc: USA
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Prisoner#1] 1
#22052053 - 08/06/15 07:15 AM (8 years, 5 months ago) |
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Quote:
Prisoner#1 said: how about explaining it
first explain why you add the double digit numbers together except in the last like where 57 remains, I mean 5+7=12 1+2=3, why didnt you continue, why the sudden leap to no longer following the rules you set. I see this with the numerology conspiracy nutters all the time and you are clearly no different
now, how about an explanation as to the whole, detailed if you would since you cant expect us to read your mind and take from it what all this means unless you want us to know that you can do first grade math problems
Not sure what the significance is but this is his pattern:
1 + 1 + <continue counting now at 2> = 4 1+1+2=4
1+ 1 + <continue counting now at 2> + <first answer from line above which is 4> + <continue counting now at 3> = 11 1+1+2+4+3=11
1 + 1 + <continue counting now at 2> + <first answer was 4> + <continue counting now at 3> + <second answer which was 11> + <continue counting again so we are at 4> = 26 1+1+2+4+3+11+4=26
1 + 1 + <continue counting now at 2> + <first answer 4> + <continue counting now at 3> + <second answer 11> + <continue counting now at 4> + <third answer 26> + <continue counting now at 5> = 57 1+1+2+4+3+11+4+26+5=57
I have no idea why sometimes he'll take one of the random answer like 26 and go 26 <---- 2 + 6 = 8
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HatingMeIsEasier
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Confucian]
#22053132 - 08/06/15 11:42 AM (8 years, 5 months ago) |
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It's not random.
Numbers behave exactly like molecules / cells.
Look at this picture:

Geometry is directly interconnected with anatomy.
These numbers are the reason why geometry exists.
Geometry is the only reason why anatomy exists.
So in my example, 26 is simply an individual 2 converged with an individual 6 - I know this because the max number is "9"; everything else that appears to be bigger than 9 is an illusion created by numbers 1 ~ 9 individually coming together, exactly like cells / molecules.
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Mr.GuessWork
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: HatingMeIsEasier]
#22053200 - 08/06/15 11:52 AM (8 years, 5 months ago) |
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You do know that molecules and cells behave in a random fashion, right?
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HatingMeIsEasier
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Re: Can we stop saying 3.141592653589 is more accurate than 3.14285714286? [Re: Mr.GuessWork]
#22053284 - 08/06/15 12:04 PM (8 years, 5 months ago) |
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You do know that what you call "random", is your ignorance excusing itself, right?
If cells / molecules were irrational, our bodies would be as irrational as your responses.
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