On Wed, 23 Feb 2022, Elijah Stone wrote:
indeed, for _=_ already
(The 'indeed' here is extraneous (or the 'for') is, if this is hard to parse.)
On Wed, 23 Feb 2022, Henry Rich wrote:
I am just saying that
_ = 1e300
0
is inconsistent with the definition of tolerant comparison, so further
arguments appealing to consistency are built on sand.
Henry Rich
On 2/23/2022 10:18 AM, Elijah Stone wrote:
So you do not find it inconsistent that 3j1e100=5j1e100 but 3j_~:5j_;
nor that 3j_ and 5j_ seem to represent the same thing (as evinced by *.)?
It does not seem at all inconsistent or problematic to define = such
that (x j. _) = (y j. _) (for finite, real x,y), and it does not
follow from such a definition that _ must compare equal with finite
values.
-E
On Wed, 23 Feb 2022, Henry Rich wrote:
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 <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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