JT
Posts:
436
Registered:
4/7/12
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Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 15, 2013 11:16 AM
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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:
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> > 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...
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> In NyaN, this becomes (using JT's suggested X for ten:
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> 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:
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> 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:
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> 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:
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> 11.0010010000111111011010101000100010000101101000110000...
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> becomes:
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> 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!
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