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Topic: 0.9999... = 1 that means mathematics ends in contradiction
Replies: 53   Last Post: Mar 18, 2013 9:33 PM

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JT

Posts: 1,148
Registered: 4/7/12
Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted: Mar 15, 2013 11:25 AM
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On 15 mar, 16:24, JT <jonas.thornv...@gmail.com> wrote:
> On 15 mar, 16:20, JT <jonas.thornv...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On 15 mar, 16:16, JT <jonas.thornv...@gmail.com> wrote:
>
> > > On 15 mar, 03:09, Transfer Principle <david.l.wal...@lausd.net> wrote:
>
> > > > On Mar 13, 1:25 pm, JT <jonas.thornv...@gmail.com> wrote:
>
> > > > > On 13 mar, 19:47, fom <fomJ...@nyms.net> wrote:
> > > > >  Dec NyaNTern      StandardTern
> > > > >  1   =1            01
> > > > >  2   =2            02
> > > > >  3   =3            10
> > > > >  4   =11 3+1       11
> > > > >  5   =12 3+2       12
> > > > >  6   =13 3+3       20
> > > > >  7   =21 6+1       21
> > > > >  8   =22 6+2       22
> > > > >  9   =23 6+3      100
> > > > >  10  =31 9+1      101
> > > > >  11  =32 9+2      102
> > > > >  12  =33 9+3      110
> > > > >  13  =111 9+3+1   111
> > > > >  14  =112 9+3+2   112
> > > > >  15  =113 9+3+3   120
> > > > >  16  =121 9+6+1   121
> > > > >  17  =122 9+6+2   122
> > > > >  18  =123 9+6+3   200
> > > > >  19  =131 9+9+1   201
> > > > >  20  =132 9+9+2   202
> > > > >  21  =133 9+9+3   210

>
> > > > I don't post much here any more, but I wanted to post at
> > > > least once here on Pi Day. And so, in honor of Pi Day, I
> > > > consider, how would we write the number pi in the
> > > > bijective numeration system NyaN?

>
> > > > Decimal is an interesting case, since the first zero occurs
> > > > rather late in the expansion. In standard decimal we see
> > > > that pi begins:

>
> > > > 3.1415926535897932384626433832795028841971693993751058209...
>
> > > > In NyaN, this becomes (using JT's suggested X for ten:
>
> > > > 3.1415926535897932384626433832794X2884197169399374XX581X9...
>
> > > > We notice that the string "510" becomes "4XX" in NyaN.
>
> > > > In ternary, which appear to be JT's preferred base, we have
> > > > that pi in standard ternary is:

>
> > > > 10.0102110122220102110021111102212222201112012121212001...
>
> > > > I forget how JT explained to write fractions less than 1/2
> > > > in NyaN (or, in general, less than 1/(n-1) -- it's because
> > > > of this that NyaN is awkward to use with real numbers).

>
> > > > This is what I obtained, starting with two '_' symbols:
>
> > > >  3.__31333122212331332313333332212222131111312121211331...
>
> > > > (Notice how the string 2110 becomes 1333, and the even
> > > > longer 211110 becomes 133333.)

>
> > > > Binary is an especially tricky case. We notice that with the
> > > > natural numbers in binary, only the _repunits_ are identical
> > > > in both standard and NyaN. All other naturals become one
> > > > digit shorter in NyaN compared to standard binary.

>
> > > > In fact, this rule appears to work converting binary to NyaN:
>
> > > > -- Replace the rightmost 0 with 2.
> > > > -- Drop the leftmost 1.
> > > > -- Increase all digits in between by 1.

>
> > > > With irrational numbers like pi, we simply ignore the first
> > > > statement above, since there is no rightmost digit.

>
> > > > And so we see that:
>
> > > > 11.0010010000111111011010101000100010000101101000110000...
>
> > > > becomes:
>
> > > > 11.___1121111222222122121212111211121111212212111221111...
>
> > > > Hmmm. I notice that in NyaN binary
>
> > > > ._22222222...
>
> > > > is already 1! (And to think that the OP has a problem with
> > > > .9999...=1 in decimal, compare this to ._2222...=1 in the
> > > > binary form of NyaN.)

>
> > > I am not sure if you try to mock me or is serious, if your serious you
> > > should feel a shame for your bad logic skills and Plato would probably
> > > consider your lack of IQ terryfieing for someone knowing so much math,
> > > because your futile attempt transmiting flaws from standard number
> > > system  into NyaN is just ridiculous what is  ._22222222... supposed
> > > to mean it is not a number in any notion of numbers i am aware of?

>
> > > Binary     1=.2          1/2=.1        2/2=.2       1/4=.(1)1
> > > 2/4=.
> > > (1)2           ...             ...               ...            ...
> > > Ternary    1=.3          1/3=.1        2/3=.2       1/9=.(1)1
> > > 2/9=.(1)2           1/27= .(2)1     2/27=.(2)2        1/81=.(3)1
> > > 2/81=.(3)2       .............
> > > Quaternary 1=.4          1/4=.1        2/4=.2       1/16=.(1)1
> > > 2/16=.
> > > (1)2          ...             ...               ...            ...
> > > Quinary    1=.5          1/5=.1        2/5=.2       1/25=.(1)1
> > > 2/25=.
> > > (1)2          ...             ...               ...            ...
> > > Senary     1=.6          1/6=.1        2/6=.2       1/36=.(1)1
> > > 2/36=.
> > > (1)2          ...             ...               ...            ...
> > > Septenary  1=.7          1/7=.1        2/7=.2       1/49=.(1)1
> > > 2/49=.
> > > (1)2          ...             ...               ...            ...
> > > Octal      1=.8          1/8=.1        2/8=.2       1/64=.(1)1
> > > 2/64=.
> > > (1)2          ...             ...               ...            ...
> > > Nonary     1=.9          1/9=.1        2/9=.2       1/81=.(1)1
> > > 2/81=.
> > > (1)2          ...             ...               ...            ...
> > > Decimal    1=.A          1/10=.1       2/10=.2      1/100=.(1)1
> > > 2/100=.
> > > (1)2         ...             ...               ...            ...

>
> > > This really can not be that hard to understand even for someone still
> > > in gradeschool, i think you just mocking me(have no idea why), or feel
> > > ashame for your poor logical skills.

>
> > > > Anyway, Happy Pi Day, everyone!
>
> > Dreadfull linebreaks but for anyone trying to figure NyaN out, you can
> > fix it i am not sure that transfer principle will though.

>
> Found an online tool
> Binary 1=.2 1/2=.1 2/2=.2 1/4=.(1)1 2/4=. (1)2 ... ... ... ...
> Ternary 1=.3 1/3=.1 2/3=.2 1/9=.(1)1 2/9=.(1)2 1/27= .(2)1 2/27=.(2)2
> 1/81=.(3)1 2/81=.(3)2 .............
> Quaternary 1=.4 1/4=.1 2/4=.2 1/16=.(1)1 2/16=. (1)2 ... ... ... ...
> Quinary 1=.5 1/5=.1 2/5=.2 1/25=.(1)1 2/25=. (1)2 ... ... ... ...
> Senary 1=.6 1/6=.1 2/6=.2 1/36=.(1)1 2/36=. (1)2 ... ... ... ...
> Septenary 1=.7 1/7=.1 2/7=.2 1/49=.(1)1 2/49=. (1)2 ... ... ... ...
> Octal 1=.8 1/8=.1 2/8=.2 1/64=.(1)1 2/64=. (1)2 ... ... ... ...
> Nonary 1=.9 1/9=.1 2/9=.2 1/81=.(1)1 2/81=. (1)2 ... ... ... ...
> Decimal 1=.A 1/10=.1 2/10=.2 1/100=.(1)1 2/100=. (1)2 ... ... ... ...


Does all this base belong to me, or did any ancient people use it?



Date Subject Author
3/8/13
Read 0.9999... = 1 that means mathematics ends in contradiction
byron
3/9/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
bacle
3/9/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Pfsszxt@aol.com
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
byron
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
byron
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Virgil
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
YBM
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
bacle
3/12/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Virgil
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/16/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
byron
3/16/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Transfer Principle
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/18/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/14/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
Brian Q. Hutchings
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
fom
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/9/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
J. Antonio Perez M.
3/13/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
JT
3/15/13
Read Re: 0.9999... = 1 that means mathematics ends in contradiction
harold james

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