Floor & Ceil (RPN-67 vs Excel)

[stilmant]

Hi Matt,

I'm new to this forum, so first of all, hello! I have some questions related to your post, and while I not have the answers, I find this topic very interesting.

You mentioned that "Excel gives the official answer," but I am curious about why Excel's implementation should be considered the standard. The definitions of the ceiling and floor functions are quite well-defined in mathematics.

The floor function of a real number \( x \), denoted by \( \lfloor x \rfloor \), is defined as:
$$
\lfloor x \rfloor = \max \{ n \in \mathbb{Z} : n \leq x \}
$$
This means \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \).

The ceiling function of a real number \( x \), denoted by \( \lceil x \rceil \), is defined as:
$$
\lceil x \rceil = \min \{ n \in \mathbb{Z} : n \geq x \}
$$
This means \( \lceil x \rceil \) is the smallest integer greater than or equal to \( x \).

So for your observation about the differences between Excel and RPN-67 for arguments less than 0, where you noted they disagree by -1, could you provide more specific examples? The term "disagree by -1" is a bit vague for me, and I think seeing specific numbers would help clarify this.

I am not familiar with the RPN-67, but if it is an emulator of the HP-67 calculator, I wonder if the built-in CEIL & FLOOR functions you mentioned are specific to the iOS app you're using?

Thanks