I was under the impression that there is in fact such a thing as a complete mathematical system (if you take “mathematical system” in the broader sense of “internally consistent system”), but such a system would be pretty limited and therefore rather useless.
Comment on Anon describes experience
WoodScientist@sh.itjust.works 3 weeks agoDepends on how your mathematical system is defined. In the mathematics system this teacher is using, negative numbers simply do not exist. The answer to 5-6 is the same as 5/0: NaN. Is this mathematical system incomplete? Yes. But, as has been thoroughly proven, there is no such thing as a complete mathematical system.
gandalf_der_12te@discuss.tchncs.de 3 weeks ago
SinAdjetivos@lemmy.world 3 weeks ago
The answer would still not be 0 as 0 is clearly still well defined within that system. NaN, undefined, etc. would be acceptable answers though. Otherwise you define:
for x > y, y - x = 0
Which defines that x = y
Resulting in the conditional x > y no longer being true
Also x/0 isn’t NaN. It’s just poorly defined and so in computing will often return “NaN” because what the answer is depends on the numbering system used and accidentally switching/conflating numbering systems is a very easy way to create a mathmatical fallacy like the one above.
jumping_redditor@sh.itjust.works 3 weeks ago
you clearly haven’t read IEEE 754
SinAdjetivos@lemmy.world 3 weeks ago
Have you?!?! IEEE 754 defines NaN, but also both a positive and negative zero (+0, -0) in addition to infinities such that x/+0 = ∞, x/-0 = -∞ and the single edge case ±0/±0 = NaN