On Sunday, October 1, 2017 at 12:22:43 AM UTC-7, netzweltler wrote: > Am Sonntag, 1. Oktober 2017 02:52:29 UTC+2 schrieb mitchr...@gmail.com: > > On Saturday, September 30, 2017 at 2:42:46 PM UTC-7, netzweltler wrote: > > > Am Samstag, 30. September 2017 23:14:36 UTC+2 schrieb mitchr...@gmail.com: > > > > > > > > .9 repeating and One share a sameness. They are quantities > > > > that are different by the infinitely small. > > > > .9 repeating is a transcendental One; the First quantity > > > > below one. The infinitely small difference means a shared > > > > sameness that is still not absolutely same. > > > > > > > > Mitchell Raemsch > > > > > > If there is a quantity between 0.999... and 1 > > > > At some point there needs to be next quantities with > > nothing in between. > Here you say there is a quantity in between.
It goes both ways. There are the in-betweens until they reach to smallest or infinitely small difference
Mitchell Raemsch > > > > > and, therefore, these are two different points on the number line then you should define the distance between these two points. If you don't, then your first quantity is simply undefined. > > > > > > 'infinitely small' is not a definition. > > > > It has a definition of being one divided by infinity > > It can't be divided any further. It is The Infinitely divided One. > > Their quantity difference is by the infinitely small. > > This means there are no quantities in between them. > Here you say there is no quantity in between. > > > > > >There are no two distinct points on the number line 'infinite(simal)ly' far away from each other.
You mean together with each other... with no in between. When not closest together there are in between.
> > > > > > Mitchell Raemsch > > Doesn't sound like a definition to me.
The usable definition is one divided by infinity... First quantity to exist in mathematics.
> > Do you agree that 0.999... means infinitely many commands > Add 0.9 + 0.09 > Add 0.99 + 0.009 > Add 0.999 + 0.0009 > ?? > Then following all of these infinitely many commands won?t get you to point 1. If you reached point 1 you have disobeyed those commands, because every single of those infinitely many commands tells you to get closer to 1 but NOT reach 1. > Therefore, if you want to define the position of a ?point? 0.999? on the number line, it cannot be at position 1 ? and for the same reason (?disobeying those commands?) it cannot be short of 1 nor can it be past 1. > So, if you want to measure the distance |1 ? 0.999?| you know where to start the measurement (at point 1) but you don?t know where to stop the measurement, because the position of a ?point? 0.999? is not defined on the number line.