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Topic: Matheology sqrt(-2): WM admits to unlistability of 0/1 sequences
Replies: 76   Last Post: Dec 28, 2013 7:39 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology sqrt(-2): WM admits to unlistability of 0/1 sequences
Posted: Dec 22, 2013 12:41 AM

jonas.thornvall@gmail.com wrote:

> > There are two ways of viewing 0.999..., either as a number carried out
> > to infinitley many decimal places or as the sequence of finitely long
> > decimals 0.9, 0.99,0.999, ... having the infinitiely long decimal,
> > 0.999... as its limit.
> >
> > For either interpetation, the final value differs from 1 by the amount 0.

>
> No there is no instance of iterated .999... following a zero that will add up
> to 1.

Does jonas.thornvall claim that there is any numerical difference
between 0.999... And s = sum_(n in |N) 9/10^n ?
>
> Not even after infinitly many added nines to form an infinite sequense
> whatever that can be, this is easily seen as the difference after infinitly
> many added nines still will be infinitly many zeros followed by a 1.

In my world, infinity many zeros following a decimal point make any
susequenct trailing digits irrelevant.

Or does jonas.thornvall wish to propose some nouveau theory of
infinitesmals to this discussion?
>
> You will approach 1 forever, but you will never get there.

Depends on whether one take the high road or the low road,
you clearly have taken the wrong road.

> But if we use a bijective base ten a number like 9A, .999A , 9999A, 99999999A
> all equals 1 however .999 .999... will not in a bijective base.

What in Niffflehiem is a "bijective" base? The ones I am familiar with
are all merely positive integers greater than 1.
And since only one of your "9A, .999A , 9999A, 99999999A" above contains
a point, whether decimal or bijective, three of them do NOT equal 1.
--

Date Subject Author
12/20/13 William Hughes
12/20/13 mueckenh@rz.fh-augsburg.de
12/20/13 William Hughes
12/20/13 mueckenh@rz.fh-augsburg.de
12/20/13 William Hughes
12/20/13 mueckenh@rz.fh-augsburg.de
12/20/13 Virgil
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