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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