Euler Identity in Home

[ColinJDenman]

(04-06-2014 02:11 PM)jebem Wrote:  Thanks, Joe and Peacecalc for your explanations. It makes all the sense.

(6) HP-PRIME: Needs Home mode selected, otherwise in CAS mode it gives "sin(pi)" = 0;
Even if we type "SIN(3.1415926535898) we still get a result of -2.06761537357E-13, as the inputted command is rounded in history to have just 12 digits: "SIN(3.14159265359)".
So it seems that the PRIME shows a better behavior than the HP-50G in this regard.

Thanks for your informative post. This was the kind of info I was wondering about. My initial thought was to wonder why digit precision was not substantially superior on the Prime, given the hardware capability. I also note that CAS settings include an epsilon value, but not Home.

Others seem to feel I do not recognise the inevitability of approximation in digital computation. I do, but feel a simple calculation displaying these errors questions the reliability of much more involved calculations. The calculator does not offer an estimate of the size of the error in the result. If you see a 'very' small result and discard it as approximation error, what is the purpose in having a calculator that displays 9E-499?

Since I appear to have touched a few buttons here, I'll try to refrain from responding further in this thread.