John Gabriel wrote: > On Saturday, 8 March 2014 15:37:59 UTC+2, Peter Percival wrote:
>> So is sin(x) defined to be x - x^3/3! + x^5/5! ? > > Well, no series is infinite. We can only ever write down a finite > number of terms, from which we can tell everything we need to know > about the series. > > You must remember that the Taylor series is an "approximation". In > fact, just about everything Newton did was an approximation. I > prefer to call what you think of "infinite" series, "partial series". > Infinite is a misnomer. > >> Or is the equation sin(x) = x - x^3/3! + x^5/5! proved? If the >> latter, what is the definition of sin? > > > In the New Calculus, the sine series can be written with as many > finite terms as you please. It is NEVER an approximation, but always > exact.
So sin(x) is both x - x^3/3! + x^5/5! *and* x - x^3/3! + x^5/5! - x^7/7! ?
Whether yes or no, I'd still like to know how you define sin(x).
-- Madam Life's a piece in bloom, Death goes dogging everywhere: She's the tenant of the room, He's the ruffian on the stair.