Sorry, can you explain this? To me, it makes sense to define abs(x) = sqrt(x^2) i.e. ignoring the negative solution enforces the positive result. Using that definition, abs(i+1) = sqrt((i+1)^2) = sqrt(i^2 + 2i + 1) = sqrt(-1 + 2i + 1) = sqrt(2i) != sqrt(2). The second example seems off in the same way (i.e. the answer should be sqrt(8i) instead of sqrt(8)). Am I missing something? Also, abs(i+2) = sqrt((i+2)^2) = sqrt(i^2 + 4i + 4) = sqrt(-1 + 4i + 4) = sqrt(4i + 3) which doesnt seem to follow the pattern your son described.
Also, just to point out that my understanding of absolute value is different than your sons. Thats not to say one is right and another is wrong, but there are often different ways of seeing the same thing. I would imagine that LLMs would similarly see it a different way. Another example of this is people defining PI by its relation to the circumference of a circle. Theres nothing wrong with such a definition, but its certainly not the only possible definition.
Also, just to point out that my understanding of absolute value is different than your sons. Thats not to say one is right and another is wrong, but there are often different ways of seeing the same thing. I would imagine that LLMs would similarly see it a different way. Another example of this is people defining PI by its relation to the circumference of a circle. Theres nothing wrong with such a definition, but its certainly not the only possible definition.