Help me get Function N running to get large gammas in the Twin Paradox?

Questions
1

I’ve written this twice, months apart from scratch. Failed both times. I’ll bet this is a trivial mistake! The attachment is .nb, identical to this paste, below.

(Twin Paradox)

(* dilation =tprime/time *)

(*natural units, c=1 ; v in fraction of c *)

(* At v = .999 c, etc. *)

v = 0.999;
dilation = 1/
((1 - (v^2))^0.5)

v = 0.999999;
dilation = 1/
((1 - (v^2))^0.5)

v = 0.999999999999;
dilation = 1/
((1 - (v^2))^0.5)

v = 0.999999999999999999999999;
dilation = 1/
((1 - (v^2))^0.5)

22.3663

707.107

Power::infy: Infinite expression 1/0. encountered. >>

ComplexInfinity

FullForm[dilation]

!(
TagBox[
StyleBox[
RowBox[{“DirectedInfinity”, “[”, “]”}],
ShowSpecialCharacters->False,
ShowStringCharacters->True,
NumberMarks->True],
FullForm])

dilation = N[1.000000000000000000000000/
((1.000000000000000000000000 - (0.999999999999999999999999^2))^(1/
2)), 1000]

Power::infy: Infinite expression 1/0.*10^-12 encountered. >>

ComplexInfinity

2

Hi,

this should work:

dilation = N[1/((1 - (SetPrecision[0.999999999999999999999999^2, Infinity]))^(1/2)), 1000]

It was just a little numerical problem. The term

((1.000000000000000000000000 - (0.999999999999999999999999^2))^(1/ 2))

is numerically zero:

0.*10^-12

Cheers,

Marco

3

Marco,

Thanks. 0.“24 nines” of c turns a billion years into about 12 hours!

10^9 / dilation *365 *24

Doug