It’s not a matter of accuracy even, if for any two natural numbers x < y it holds x - y = 0 then x = y, which is a contradiction. So this is basic consistency requirement, basically sabotaging any effort to teach kids math.
Depends 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.
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.
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
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.
It’s not a matter of accuracy even, if for any two natural numbers x < y it holds x - y = 0 then x = y, which is a contradiction. So this is basic consistency requirement, basically sabotaging any effort to teach kids math.
Depends 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.
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.
you clearly haven’t read IEEE 754
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
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.