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Joe Horn · (This post was last modified: 04-16-2014 09:52 PM by Joe Horn.)

Manolo! Good news! I think I figured out a solution to the root cause of our disagreement! (Details below) Meanwhile, back at the ranch...

(04-16-2014 12:29 PM)Manolo Sobrino Wrote: Joe, I don't know what to do when people just don't read the posts in the thread.

Sorry that I came across that way! I really have read them all, but I think we've been on different wavelengths, or in alternate universes, or something. But I'm trying. ("Yes... very trying." -- my brother Jim)

(04-16-2014 12:29 PM)Manolo Sobrino Wrote: Maybe it's so obvious for me that I'm just incapable of explaining it to you.

Two quotes come to mind:

Joe, the fact that something is obvious to you does not mean that it is obvious to everybody. -- Richard Nelson, during a friendly debate many years ago.

"Because it's obvious" is not an acceptable mathematical proof. -- Mr. Santo Formolo, my favorite high school math teacher.

(04-16-2014 12:29 PM)Manolo Sobrino Wrote: At least I hope that you understand now why Wolfram Alpha gives you that 0.*10^-12 "Result".

AHA! (Light bulb lights up!) Try both of these in Wolfram Alpha:

sin(3.14159265359)
sin(314159265359/10^11)

The first one is assumed to be the sine of an approximate value, hence the zero "result" (notice that it does not say "exact result"), rounded the way you've been saying it should be rounded, and you're correct, and nobody has denied that... IFF it's an approximate input.

[Image: wolframalpha0.png]

The second one is assumed to be the sine of an exact value, hence the "exact result" with its humongous "decimal approximation", and even offering a "more digits" button since the result IS exact and has an infinite number of CORRECT digits:

[Image: wolframalpha.png]

Bottom line: I think we're both right. (yay) You're right that approximate inputs should not yield results with more "precision" than the input (because GIGO), and I'm right that exact inputs do in fact have exact results which can and should be computed. The only difference is that TI ASSUMES the former for sin(3.14159265359), and HP ASSUMES the latter for sin(3.14159265359). Neither assumption is always correct; whether it's correct or not depends entirely on the user's intentions. Hence using EITHER tool correctly requires that the user understand how the tool works and what its assumptions are. Can we agree on at least that much? (I hope so!)