JT
Posts:
1,306
Registered:
4/7/12


Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted:
Mar 15, 2013 11:25 AM


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/(n1)  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?

