Thanks for the detailed explanation and for the counterexample to my
argument.
It seems that I haven't thought carefully how the "=" operates behind the
scenes when comparing two complex numbers.
Best regards,
---
Michail L. Liarmakopoulos, MSc
On Wed, Feb 23, 2022, 13:03 Elijah Stone <elro...@elronnd.net> wrote:
> Two arguments:
>
> 1. Comparison is tolerant anyway. So:
>
> 3j1e100 = 5j1e100
> 1
>
> Since _ is greater than 1e100, the (relative) difference between 3j_ and
> 5j_ should be less than that between 3j1e100 and 5j1e100
>
> 2. Infinity is, of course, not a number. So, when encountering an
> expression involving infinity, it is necessary to ask how it should be
> interpreted. One way to interpret 3j_ is as follows: the limit as y
> approaches _ of 3 j. y. Well, that does not converge. But its _angle_
> does, as does the angle of 5 j. y, and they converge to the same result:
> 0.5p1. The j interpreter is kind enough to tell us as much:
>
> 0.5p1 =!.0 {:"1*.3j_ 5j_
> 1 1
> 3j_ -:!.0&*. 5j_
> 1
>
> (The fact that these expressions evaluate to 1 even with a comparison
> tolerance of 0--and would continue to do so, even given infinite
> precision--is my argument for why 3j_=5j_ should be 1 even with a
> comparison tolerance of 0. I recognise, however, that there are other
> tradeoffs involved, and this may not be the right choice; but I think
> there is no excuse for a 0 result given nonzero comparison tolerance,
> unless _=_ is changed.)
>
> -E
>
> On Wed, 23 Feb 2022, Michail L. Liarmakopoulos wrote:
>
> > It seems correct to me, as they're two different complex numbers. If they
> > were the same:
> >
> > 5j_=5j_
> > 1
> >
> >
> > They have the same modulus though:
> >
> > %: 9 + _
> >
> > _
> >
> > %: 25 + _
> >
> > _
> >
> > (|3j_) = (|5j_)
> >
> > 1
> >
> > Best,
> >
> > ---
> > Michail L. Liarmakopoulos, MSc
> >
> > On Wed, Feb 23, 2022, 10:15 Elijah Stone <elro...@elronnd.net> wrote:
> >
> >> 3j_ = 5j_
> >> 0
> >>
> >> I think it should be 1. For nonzero comparison tolerance, at any rate.
> >>
> >> -E
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