HP-71B: 1^Inf Error

[Valentin Albillo]

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Hi, Jean-François,

(06-09-2023 08:17 AM)J-F Garnier Wrote:  I only recently noticed that the HP-71B is raising an error when attempting to calculate 1^Inf. [...] I'm more curious of the reasons of the HP-71B development team: pure mathematical considerations or implementation constraints?

That, no one can know unless the development team left behind some notes/docs about it, or if the System source code includes comments on the implementation, which I haven't checked.

The HP-71B is a marvel in so many aspects but it has some glaringly bad decisions inflicted upon it, I posted some of the most egregious ones here, and left several others for another occasion.

One of them is the whole IEEE implementation, which no one in the users' base needed or asked for, and which only succeeded in adding unwanted complexity to the math functions implementation in assembler, also taking lots of ROM space to implement in the System and Math ROMs (and probably others), space which could've been put to much better use, and further slowing down the computations. I've extensively used the 71B for decades doing engineering and technical computations and not even once did I need its IEEE abilities. Positive zero ? Negative 0 ? For real-life applications ? Seriously ?

This preamble is just to make it clear that the development team did some very poor decisions, perhaps influenced by people at HP not belonging to the team and perhaps even dismissive of the HP-71B overall, and returning an Error for 1^Inf is one of those poor decisions.

In this thread, people are talking all the time of "limits" and "approaching" and such, but in fact none of that applies to this case because in 1^Inf we don't have the base "approaching" 1 or being 1 "in the limit", we have the plan, exact constant 1, and constants do not vary nor do they tend to some limit last time I checked.

When raising the exact constant 1 to the power of 100, 1000, one million, a Googolplex or Googolplex! (factorial), we don't get a result that approaches 1, we get exactly 1 every time, all the time, period. Thus, it's clear that 1^Inf can be safely and logically defined as 1, so the HP-71B should have returned 1 as a default value, perhaps with an overridable Warning for the squimish, but never ever Error.

Best regards and have a nice finde.
V.