But ←→ is used in maths, too.
In the realm of logic, let φ and ψ be formulæ.
If φ ←→ ψ is a tautology (in semantic parlance “is always true”)
then φ and ψ may always be substituted for each other
regardless of “circumstances” or “surrounding constraints.”
So using that symbol (I don’t know to reproduce it so I spelled it
using two glyphs¹) actually /should/ be understood that way.
And even if that wasn’t the case, as a matter of fact, it regularly
gets interpreted that way so it wouldn’t be very helpful to tell
everyone they got the interpretation wrong. Rather, we should strive
to make ourselves easily understood in the first place.
So I’d plead in favor of either explicitly adding the verb rank
or not trying to give equivalent forms to start with. I prefer
the former, but maybe I’ll dig for the visualizations I created
some years ago and finally add them to the @,@:,&,&: pages.
¹ I could have copied it over from Pascal’s message but
Raul already wilfully ignored that one
(that’s my personal reading, and not meant as an offense:
there can be good value in doing so, and I join that game)
Am 28.06.22 um 01:23 schrieb Raul Miller:
On Mon, Jun 27, 2022 at 5:58 PM Elijah Stone <elro...@elronnd.net> wrote:
as I understand it, this left-right arrow is used in math to symbolize "if
and only if"
The iff arrow uses two bars, cf ⟺ .
... But, here, it's worth noting that math relies heavily on contextual
constraints, and that we routinely and explicitly ignore concepts which
would conflict with those surrounding constraints.
Yes. And in apl context, the symbol ↔ means 'can be substituted for' or 'is
equivalent to'.
Ok, thanks.
That said, I would consider "rank" as being analogous to "domain", and
the use of left right arrow in (for example) an integer domain does
not mean that the equivalence holds in a complex domain (let alone a
vector domain).
Anyways, thanks for the clarification,
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