Re the matter of the index origin in J being 0, you may find of interest the article “Neumbering”, by O. G. Cassani & John Horton Conway, from the 40th anniversary issue of “The Mathematical Intelligencer”:
https://link.springer.com/article/10.1007%2Fs00283-017-9720-3 This proposes a resolution of the issue of what to call the initial element of an ordered list if you are using index origin 0 (as in J). —— Murray Eisenberg mur...@math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 240 246-7240 (H) University of Massachusetts 710 North Pleasant Street Amherst, MA 01003-9305 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm