JT
Posts:
1,386
Registered:
4/7/12


Re: 1/3 partitioned expansion in different bases
Posted:
Feb 2, 2013 1:41 AM


On 2 Feb, 07:07, JT <jonas.thornv...@gmail.com> wrote: > On 2 Feb, 06:45, JT <jonas.thornv...@gmail.com> wrote: > > > > > > > > > > > On 1 Feb, 15:06, Frederick Williams <freddywilli...@btinternet.com> > > wrote: > > > > JT wrote: > > > > And 0.999... would be expressed as 0.3 or.......? > > > > What are you asking? Does 0.9 recurring (in base 10) have the same > > > value as 0.3 (in base 3)? No, 0.9 recurring (in base 10) has the same > > > value as 1.0 (in base 3). > > > >  > > > When a true genius appears in the world, you may know him by > > > this sign, that the dunces are all in confederacy against him. > > > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting > > > Well actually in this numbersystem in base 3 > > 0,3=1 > > This means that 0,3 actually completes 0.999... in standard digit > > expansion, it is the sum of all possible fractions of a single natural > > number. > > > So in my bases a single natural actually equals the sum of all > > fractions thus 1=0,3 in base 3 the decimal expansion is complete. > > In reality though you will never use it since 3/3 equals one. Base 3 In fact 1,3=2 You may find funny, but it is not that strange, the fractions have completness, but of course in reality you never write 1,3 you write 2.

