3 ms·
Would you consider -3 a number? It's certainly not a measure of quantity. A better way of thinking about it is that it's 2 things: a magnitude and a direction.
by injb 6y ago
Would you consider -3 a number? It's certainly not a measure of quantity. A better way of thinking about it is that it's 2 things: a magnitude and a direction. Complex numbers just expand the direction into two dimensions. As long as you accept negative numbers, then you already accept the fact that there can be more than one number of a given size. The complex numbers just contain infinitely many numbers of a given size, instead of only 2.
- gpm 6y agoIn plain english, no I don't think I would particularly consider -3 a number. If I say someone gave me a number of horses I don't mean they stole my horse. I think it is the right call to include them in the mathematical definition though. Unlike complex numbers they are almost always useful (they are needed to turn the object into a field, which is needed if you want everyday operations like subtraction to always remain within the set), have a much more intuitive definition of multiplication, are a smaller generalization, etc.