Why won't the prime graph correctly?

05232019, 03:42 PM
Post: #7




RE: Why won't the prime graph correctly?
(05232019 09:14 AM)Aries Wrote: Quite the contrary, teachers know very well what they are teaching, calculators are stupid and/or badly programmedI suppose different people have different opinions. Here are what the four calculators with me at school (I teach Physics) today say:
On a calculator that can handle complex numbers, the complex result is what I would expect. If a calculator tells me that \((1)^{1/3}\) is \(1\), I don't know what result it will give me for \((1\pm{\bf i}\epsilon)^{1/3}\). The cut in the complex plane must be somewhere unusual. On a calculator that handles only real numbers, I prefer an error. The problem is that when the power is a real number  for example, \(0.4\)  a calculator that tries to give a real answer must first turn the power into a rational number, express it in its lowest terms, and then throw an error only if the denominator is even. The Casio appears to do this  \((1)^{0.4}\) gives 1, powers of 0.401 up to 0.407 give Math Error, and a power of 0.408 gives 1. It's logical, it's consistent, but is it sensible? I think that to put the Prime's behaviour down to being "badly programmed" is to miss the point. There is a conceptual difference between a fractional power and an integral nth root: whether to ignore this difference, or if not, how to address it, aren't trivial questions. I think the Prime gets it right by having two separate functions, each behaving as I'd expect. If I were a maths teacher teaching fractional powers at a basic level, I might prefer the behaviour of the Casio. I'm surprised to hear that the TI NSpire appears to follow the Casio  is there a complex mode that needs to be turned on, and if so, does this change the behaviour? Nigel (UK) 

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