HP PRIME not raising overflow/underflow may cause critical errors

[Han]

(03-20-2021 02:28 AM)robve Wrote:  LOL

I was a teenager in the 80s and very lucky to have a Philips P2000T "home computer" and an Apple ][e. I got up at 7am in weekends to program my own BASIC concoctions and some games from magazines and later BASICODE broadcast on the radio. Can you believe it?

The P2000T Microsoft BASIC interpreter did this:

? 0↑0
1

Hmmm... this did not make much sense to me at first, because 0↑n=0 too and both cannot be true at the same time, right?

$$ \left. \begin{array}{l} 0^n = \underbrace{0\cdot 0\cdots 0}_\text{$n$ times} = 0 \cr x^0 = 1 \end{array} \right\} 0^0 = ? $$

This is not a matter of debate or a "current consensus among mathematicians". It is undefined. Just look at the expression above and you will never forget. Period. End of story.

- Rob

Context makes a huge difference in mathematics, though. And depending on the context, it may be 1, or 0, or undefined. It is defined in those contexts by choice in order to have a consistent system. Hence the "consensus." The wikipedia link gives plenty of well-reasoned examples of why they can be taken as any of these. Here is another resource:

https://www.maa.org/book/export/html/116806

EDIT: Also, your explanation is in fact not mathematically sound. For \( 0^n \) your assumption is that \( n \) is a positive integer. And what does it mean to write "zero" copies of the number 0 prior to multiplying? For \( x^0 \), is \(x \) assumed to be a real positive number? Apples and oranges. The former is a discrete problem while the latter is an analytical problem.