[ExI] speed of light at the speed of light

[Anders Sandberg]

On 2013-08-23 18:52, Gordon wrote:
> Adrian Tymes <atymes at gmail.com> wrote:
>
> >That last sentence is unclear.  What do you mean by ".999...1"?
>
> I think it is a fact of mathematics that .99... carried out to an 
> infinite number of 9s is equal to 1.  No?

Yes, the symbolic meaning of "0.9999..." corresponds to the real number 
1. It if one of the less well known facts that the number system we use 
actually has non-unique number representations. Causes no end of 
internet debates.

>
> If true then when I say "in the limit when I approach c" it means that 
> in the limit I am travelling at c. Or at least I don't see the difference.

"In the limit" is a bit subtle. It does not mean that "in the limit of x 
approaching y" x becomes exactly y, only that x becomes as close to y as 
anybody can wish. "1/x goes to infinity in the limit as a positive x 
approaches zero" does not mean 1/0 *is* infinity (especially since stuff 
goes more and more negative if you approach from the negative side).



-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

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