cool-RR wrote: > Chris, why is this invariant `div*y + mod == x` so important? Maybe it's > more important to return a mathematically reasonable result for the the > floor-division result than to maintain this invariant?
You keep talking about floor(inf) == inf being "mathematically reasonable", but I'm not convinced that it is. Can you justify why you think it is mathematically reasonable? Remember that IEEE-754 inf represents two different concepts: (1) A large but finite number which has overflowed. (2) Actual mathematical infinity ∞. Even in the case of actual mathematical infinity[1], the result of floor(∞) isn't clear to me. Floor is supposed to return an integer, how do you know that ∞ is integer valued? You can do ∞ % 1 to see what the fractional part is, but that gives NaN, so justify your belief that ∞ is integer-valued. [1] But *which* mathematical infinity? One of the cardinal infinities, the alephs, or one of the ordinal infinities, the omegas and the epsilons? (There are an infinite number of *all three*.) Is c just another name for aleph-1, or is distinct from all the alephs? Even professional mathematicians tread warily when doing arithmetic on infinities. -- Steven -- https://mail.python.org/mailman/listinfo/python-list
