0^0 = 1?

[emece67]

(04-26-2017 06:40 AM)Paul Dale Wrote:  The WP 34S conforms to ISO/IEC 9899:2011 for real and complex arguments.

I've read what such ISO standard states about the pow() function and it mandates some objectionable (to me) results, such as:

• \(0^0 = 1\)
• \(1^\infty = 1\)
• \(1^{-\infty} = 1\)
• \(1^{NaN} = 1\)
• \(\infty^0 = 1\)
• \((-\infty)^{-0.5} = 0\)
• \((-\infty)^0 = 1\)
• \((-\infty)^{0.5} = \infty\)
• \((-\infty)^\infty = \infty\)
• \(NaN^0 = 1\)
• \((-1)^0 = 1\)
• \((-1)^\infty = 1\)
• \((-1)^{-\infty} = 1\)
  

As Paul stated, the wp34s conforms to this standard (I've checked it).

But, despite the 9899 standard, is this the way people expect a calculator to behave? Apart from the, long discussed, \(0^0\) case, I expected NaN in all cases.

What is the rationale behind such behavior?

Regards.

Note. The pow() function takes two float/double arguments, there is no pow() function for integers, so I think we will only discuss the real case.