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#1 2013-01-04 18:38:00

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Number Theory Official Topic

Infinity and other cool things about it is too narrow for me.

I like number theory.  For example, 0.99999999... is 1.  And 0.000000000....01 is 0.  And Tau should replace Pi.

List of sources:
Khan Academy
A bunch of books.


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#2 2013-01-04 18:48:28

mythbusteranimator
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Registered: 2012-02-28
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Re: Number Theory Official Topic

Nao

Tau No Better Dahn Pi


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#3 2013-01-04 20:45:35

RedRocker227
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Re: Number Theory Official Topic

0.9999... doesn't equal one


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#4 2013-01-04 20:47:10

zubblewu
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Registered: 2011-02-17
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Re: Number Theory Official Topic

depends on what youre using it for and how you're using it
sometimes it is
sometimes it isnt


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#5 2013-01-04 20:49:52

RedRocker227
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Re: Number Theory Official Topic

I don't understand

How is it sometimes equal and sometimes not

Last edited by RedRocker227 (2013-01-04 20:50:12)


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#6 2013-01-04 20:52:39

Mokat
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Registered: 2011-12-08
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Re: Number Theory Official Topic

pi ftw


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#7 2013-01-04 20:53:42

zubblewu
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Re: Number Theory Official Topic

depends on what kind of math
our number system(s) are just simple like that


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#8 2013-01-04 20:55:01

RedRocker227
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Registered: 2011-10-26
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Re: Number Theory Official Topic

Why does tau have to replace pi
What's wrong with having both


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#9 2013-01-04 20:57:30

zubblewu
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Registered: 2011-02-17
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Re: Number Theory Official Topic

the fact that it would be a bit redundant
we couldnt have that could we!


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#10 2013-01-04 21:04:22

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

RedRocker227 wrote:

0.9999... doesn't equal one

How so?  I can give proof of it.


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#11 2013-01-04 21:11:10

RedRocker227
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Re: Number Theory Official Topic

Firedrake969 wrote:

RedRocker227 wrote:

0.9999... doesn't equal one

How so?  I can give proof of it.

Okay then


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#12 2013-01-04 21:11:13

777w
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Registered: 2009-02-10
Posts: 1000+

Re: Number Theory Official Topic

0.9999 etc is nearly one, but therell always be an infinitely small piece missing
of course you could always dismiss this infinitely small piece as "zero" but whats the fun in that?
also if 0.9999 etc is one then what about 1/3 and other fractions which produce repeating decimals

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#13 2013-01-04 21:15:20

RedRocker227
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Registered: 2011-10-26
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Re: Number Theory Official Topic

Hm although I kind of contradicted myself
In another thread I said 0.000...1 doesn't exist, so then what would 1-0.999 be
Hmmmm


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#14 2013-01-04 21:17:54

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

RedRocker227 wrote:

Firedrake969 wrote:

RedRocker227 wrote:

0.9999... doesn't equal one

How so?  I can give proof of it.

Okay then

I'd like your explanation first.

777w wrote:

0.9999 etc is nearly one, but therell always be an infinitely small piece missing
of course you could always dismiss this infinitely small piece as "zero" but whats the fun in that?
also if 0.9999 etc is one then what about 1/3 and other fractions which produce repeating decimals

By the definition of infinity, you can't have that 1 at the end because of the infinite 0s.
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
Substitution:
0.333.... + 0.666.... = 0.9999...

RedRocker227 wrote:

Hm although I kind of contradicted myself
In another thread I said 0.000...1 doesn't exist, so then what would 1-0.999 be
Hmmmm

0.

Last edited by Firedrake969 (2013-01-04 21:27:00)


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#15 2013-01-04 21:20:10

777w
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Registered: 2009-02-10
Posts: 1000+

Re: Number Theory Official Topic

Firedrake969 wrote:

zubblewu wrote:

0.9999 etc is nearly one, but therell always be an infinitely small piece missing
of course you could always dismiss this infinitely small piece as "zero" but whats the fun in that?
also if 0.9999 etc is one then what about 1/3 and other fractions which produce repeating decimals

By the definition of infinity, you can't have that 1 at the end because of the infinite 0s.
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
Substitution:
0.333.... + 0.666.... = 0.9999...

zubblewu didnt write that

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#16 2013-01-04 21:27:47

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

777w wrote:

Firedrake969 wrote:

zubblewu wrote:

0.9999 etc is nearly one, but therell always be an infinitely small piece missing
of course you could always dismiss this infinitely small piece as "zero" but whats the fun in that?
also if 0.9999 etc is one then what about 1/3 and other fractions which produce repeating decimals

By the definition of infinity, you can't have that 1 at the end because of the infinite 0s.
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
Substitution:
0.333.... + 0.666.... = 0.9999...

zubblewu didnt write that

Now he did.  c:  Fixed.


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#17 2013-01-04 21:33:43

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

Plants use golden ratio + Fibonacci numbers.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. for those who don't know it.  THe ratio between 2 consecutive #s comes closer to 1.61..... the higher you go.


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#18 2013-01-04 21:44:04

Wes64
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Registered: 2011-08-19
Posts: 1000+

Re: Number Theory Official Topic

Firedrake969 wrote:

By the definition of infinity, you can't have that 1 at the end because of the infinite 0s.
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
Substitution:
0.333.... + 0.666.... = 0.9999...

thats a good method to prove this.


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#19 2013-01-04 21:45:25

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

Wes64 wrote:

Firedrake969 wrote:

By the definition of infinity, you can't have that 1 at the end because of the infinite 0s.
1/3 = 0.333...
2/3 = 0.666...
3/3 = 1
Substitution:
0.333.... + 0.666.... = 0.9999...

thats a good method to prove this.

Thank you.


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#20 2013-01-04 21:50:45

RedRocker227
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Registered: 2011-10-26
Posts: 1000+

Re: Number Theory Official Topic

Too lazy to quote and crop the unrelated bits since I'm on my iPod and it takes ages but
Where you said (1/3)+(2/3)=3/3=0.333...+0.666...=0.999...=1, that's incorrect since I'd've thought there's no true value for 1/3, only approximations, I'm not entirely sure though

I'm still kind of undecided though, as far as I know there's no official answer and it's down to which set of proofs you believe basically

Last edited by RedRocker227 (2013-01-04 21:51:29)


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#21 2013-01-04 21:54:16

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

RedRocker227 wrote:

Too lazy to quote and crop the unrelated bits since I'm on my iPod and it takes ages but
Where you said (1/3)+(2/3)=3/3=0.333...+0.666...=0.999...=1, that's incorrect since I'd've thought there's no true value for 1/3, only approximations, I'm not entirely sure though

I'm still kind of undecided though, as far as I know there's no official answer and it's down to which set of proofs you believe basically

Actually, 1/3 is a repeating decimal number, so it would be exactly 0.333333.... if you can call it exact.


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#22 2013-01-04 21:59:37

RedRocker227
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Registered: 2011-10-26
Posts: 1000+

Re: Number Theory Official Topic

Firedrake969 wrote:

RedRocker227 wrote:

Too lazy to quote and crop the unrelated bits since I'm on my iPod and it takes ages but
Where you said (1/3)+(2/3)=3/3=0.333...+0.666...=0.999...=1, that's incorrect since I'd've thought there's no true value for 1/3, only approximations, I'm not entirely sure though

I'm still kind of undecided though, as far as I know there's no official answer and it's down to which set of proofs you believe basically

Actually, 1/3 is a repeating decimal number, so it would be exactly 0.333333.... if you can call it exact.

But there's no correct way to write down 1/3 other than as a fraction, IMO that means you shouldn't be able to use what you claim to be its decimal equivalent in an equation or proof


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#23 2013-01-04 22:35:11

lalala3
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Registered: 2008-10-03
Posts: 100+

Re: Number Theory Official Topic

RedRocker227 wrote:

0.9999... doesn't equal one

Yes it does. Allow me to prove it.
Let x=0.99999999...
Therefore, 10x=9.999999999...
Minus x equals 9
So, 10x-x=9, or 9x=9. x equals one.

RedRocker227 wrote:

Firedrake969 wrote:

RedRocker227 wrote:

Too lazy to quote and crop the unrelated bits since I'm on my iPod and it takes ages but
Where you said (1/3)+(2/3)=3/3=0.333...+0.666...=0.999...=1, that's incorrect since I'd've thought there's no true value for 1/3, only approximations, I'm not entirely sure though

I'm still kind of undecided though, as far as I know there's no official answer and it's down to which set of proofs you believe basically

Actually, 1/3 is a repeating decimal number, so it would be exactly 0.333333.... if you can call it exact.

But there's no correct way to write down 1/3 other than as a fraction, IMO that means you shouldn't be able to use what you claim to be its decimal equivalent in an equation or proof

That's why we use repeater bars. It's not like we're actually going to use it, or anything, for that matter, as a decimal for serious math.

Last edited by lalala3 (2013-01-04 22:37:34)


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#24 2013-01-04 22:36:09

Firedrake969
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Registered: 2011-11-24
Posts: 1000+

Re: Number Theory Official Topic

lalala3 wrote:

RedRocker227 wrote:

0.9999... doesn't equal one

Yes it does. Allow me to prove it.
Let x=0.99999999...
Therefore, 10x=9.999999999...
Minus x equals 9
So, 10x-x=9, or 9x=9. x equals one.

Thanks for another proof.  :>


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