JT
Posts:
436
Registered:
4/7/12
|
|
Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 15, 2013 11:20 AM
|
|
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.
|
|
