[Jprogramming] Complex tolerant comparison

[Henry Rich]

As the essay points out, according to the rules _ is tolerantly equal to 
everything.  To avoid that, comparisons to _ are intolerant.

Henry Rich

On 2/23/2022 7:09 AM, Elijah Stone wrote:
> https://code.jsoftware.com/wiki/Essays/Tolerant_Comparison
>
> A good read, explains the workings of the comparators.
>
>  -E
>
> On Wed, 23 Feb 2022, Michail L. Liarmakopoulos wrote:
>
>> 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 <elronnd at 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 <elronnd at elronnd.net> wrote:
>>> >
>>> >>     3j_ = 5j_
>>> >> 0
>>> >>
>>> >> I think it should be 1.  For nonzero comparison tolerance, at any 
>>> rate.
>>> >>
>>> >>   -E
>>> >> 
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