This shows that there are only two real problems in computer science:
- Giving things proper names
- Documenting code after the code has been written
- Off by one errors
:P
From the candidates, I somewhat like mrkn's suggestion here:
lower-unbounded range
I am not sure if it is an ideal candidate, but to me it conveys
a similar meaning as "beginless", in that it refers to the
"lower" area of a range - well, the part where it all begins. :P
(You can also use left/right, but I think if we only compare
lower/upper to left/right, to me lower/upper makes a bit more
sense than left/right, within this context.)
Note that I find "beginningless" to be a very clumsy word as well.
Obviously that word exists (example: https://en.wiktionary.org/wiki/beginningless)
but I find it ... awkward.
I do not have any real preference either way so, to be completely honest,
I am with mame here - I don't think it is that important, at the least not
that I would dwell that much thought on it. Thinking about good names is
often quite difficult - just look at HashWithIndifferentAccess.