# [time 682] Re: [time 680] Re: [time 678] Re: [time 676] Reply to NOW/PAST question

Mon, 6 Sep 1999 16:12:12 +0900

Dear Stephen,

There is another quantitative difference between them:

> > What is the difference? Does it diverge or converge or neither as x ->
> > \infinity?
>
> 1/(1-x) = 1+x+x^2+x^3+x^4+...
>
> converges for |x|<1, but diverges for |x|>1, while
>
> exp(x) = 1+ x + x^2/2! + x^3/3! + x^4/4! + ...
>
> converges for all (complex (or operator)) x. No need to say that they have
> different values for the same value of x ... ?

The former diverges as |x| -> 1 with |x| < 1, while the latter converges for
all x. The former corresponds to the divergence of 1/(1-v^2/c^2) when v/c -> 1
with |v|/c < 1. The latter then would mean that in the QM world the speed of
things can be infinite.

Best wishes,
Hitoshi

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