4 ms·

Imaginary numbers are also continuous, are they not?

• gpm 6y ago
  So they are, so are many other spaces. I'd avoid calling complex numbers "numbers" personally. In the context of plain english (and not currently in the context of mathematics) I think of the word "number" as saying that this is somehow a measure of a quantity (We have "a number" of brands of cereal in the store). Complex numbers are not a measure of a quantity. I'd probably replace the "numbers" part with "field". I don't have a good replacement for the "complex" part, but I think that should change also (because telling people things are complex is almost as bad as telling them that they are imaginary). If no one proposed something better and I was king of the universe I guess I'd just name them after whoever discovered them.
  • 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 ago
      In 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.