Hello, Seems I've sent the following two emails to the wrong email address. Forwarding.
TLDR: are there any plans implementing new features in the arithmetic with infinities so that the indeterminate forms mentioned at the Wolfram Mathworld link below return _. ? For example: 0%0 and _%_. Best regards, Michail --- Michail L. Liarmakopoulos, MSc ---------- Forwarded message --------- From: Michail L. Liarmakopoulos <[email protected]> Date: Fri, Jan 21, 2022, 08:13 Subject: Re: A question on _. and infinities To: <[email protected]> Hello again, Apologies but the corresponding calculations to the 7 forms of indeterminate expressions are the following: ```j 0%0 NB. 0/0 0 NB. Result: 0, should have been _. 0*_ NB. 0*Infinity 0 NB. Result: 0, should have been _. _%_ NB. Infinity/Infinity |NaN error NB. Result: NaN error, should have been _. | _ %_ _-_ NB. Infinity - Infinity |NaN error NB. Result: NaN error, should have been _. | _ -_ 0^0 NB. 0^0 1 NB. Result: 1, should have been _. _^0 NB. Infinity^0. 1 NB. Result: 1, should have been _. 1^_ NB. 1^Infinity 1 NB. Result: 1, should have been _. ``` Best regards, On Fri, Jan 21, 2022 at 8:04 AM Michail L. Liarmakopoulos < [email protected]> wrote: > Hello all, > > I've been playing around with infinities _ and __ in my j903 interpreter. > > Most of the time it works as it should, mathematically. Examples: > > ```j > 1-_ NB. 1 - Infinity > __ NB. Result: -Infinity, correct. > > 1+_ NB. 1 + Infinity > _ NB. Result: Infinity, correct. > > 1%0 NB. 1/0 > _ NB. Result: Infinity, correct. > > -1%0 NB. -1/0 > __ NB. Result: -Infinity, correct. > > 1%_ NB. 1/Infinity > 0 NB. Result: 0, correct. > > _+_ NB. Infinity + Infinity > _ NB. Result: Infinity, correct. > > _-__ NB. Infinity - (-Infinity) > _ NB. Infinity, correct. > > _*_ NB. Infinity*Infinity > _ NB. Infinity, correct (I guess). > ``` > I know that the indeterminate form _. shouldn't be used in general, > besides a placeholder for a bad formatted data or for missing values in our > data (as mentioned in this article > <https://code.jsoftware.com/wiki/Vocabulary/underdot>), but I was > wondering if you have any plans of extending the arithmetic with > infinities, in such a way that the following operations would return the > indeterminate form (taken from Wolfram Mathworld > <https://mathworld.wolfram.com/Indeterminate.html>): 0%0, 0*_ , _%_, _-_, > 0^0 and _^0, 1^_ . > > Here are the values I get for the above, that are not correct > mathematically (but I suppose they have a certain reasoning behind them, > returning the values they do return): > > ```j > _ - _ NB. Infinity - Infinity > |NaN error NB. Result: NaN error, should have been (?) _. > | _ -_ > > _%_ NB. Infinity/Infinity > |NaN error NB. Result: NaN error, should have been (?) _. > | _ /_ > > 0^0 NB. 0^0 > 1 NB. Result: 1, should have been (?) _. > > 0%0 NB. 0/0 > 0 NB. Result: 0, should have been (?) _. > > _^_ NB. Infinity^Infinity > _ NB. Result: Infinity, should have been (?) _. > ``` > > Best regards, > > -- > Michail L. Liarmakopoulos, MSc > Linkedin <https://www.linkedin.com/in/mlliarm/> > -- Michail L. Liarmakopoulos, MSc Linkedin <https://www.linkedin.com/in/mlliarm/> ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
