4 ms·

What does it mean to multiply two points in the plane? You still need an additional rule for that.

enriquto 8y ago
> What does it mean to multiply two points in the plane? You still need an additional rule for that. yes, you do. I was answering the question of what complex numbers are. There are many things that you can do with them, that you need to define separately.
- ttoinou 8y ago
  a 2D point is not enough to define complex numbers
  - enriquto 8y ago
    > a 2D point is not enough to define complex numbers alright. Yet, one 2d point is certainly enough to define one complex number, which is what I meant. The data is the same, but they have different methods.
    - navane 8y ago
      I struggle with this a lot, too. Maybe "complex numbers" is a misnomer, and we should call them "complex operations", or "complex methods". I have a hunch that for math people complex numbers are tied really close to the operations you perform with them. But to me, the lay man, the numbers are just data. From reading around on HN I infer that there are certain things that are grouped together because they share certain actions. Groups, sets, monads. However, if you were to encounter the number (1, 5) in the wild, you wouldnt know if it was a complex number or just a 2 dimensional vector until it is operated upon.
    - ttoinou 8y ago
      The OP was looking for "explanation of complex numbers" You won't explain anything by talking about 2D points only But you can if you specify only how they behave with addition and multiplication (see my others posts)
      - enriquto 8y ago
        > The OP was looking for "explanation of complex numbers" > You won't explain anything by talking about 2D points only The OP was complaining about the explanation that complex numbers "have a real and an imaginary part", because it mean nothing to them. It is alright, then, to clarify that this just means that they are points in the plane, and some operations will be defined on these points.
        ttoinou 8y ago
        Yes
- darkscape 8y ago
  Hmm, I tend to think that what one can do with some objects is an essential part of what they are. Two-dimensional vectors can just as well be thought of as points in the plane. What sets complex numbers apart is eg that we define complex multiplication of them. A more general example: a group is not just some set G, but that set with a binary operation satisfying certain axioms.

> What does it mean to multiply two points in the plane? You still need an additional rule for that. yes, you do. I was answering the question of what complex numbers are. There are many things that you can do with them, that you need to define separately.

ttoinou 8y ago
a 2D point is not enough to define complex numbers
- enriquto 8y ago
  > a 2D point is not enough to define complex numbers alright. Yet, one 2d point is certainly enough to define one complex number, which is what I meant. The data is the same, but they have different methods.
  - navane 8y ago
    I struggle with this a lot, too. Maybe "complex numbers" is a misnomer, and we should call them "complex operations", or "complex methods". I have a hunch that for math people complex numbers are tied really close to the operations you perform with them. But to me, the lay man, the numbers are just data. From reading around on HN I infer that there are certain things that are grouped together because they share certain actions. Groups, sets, monads. However, if you were to encounter the number (1, 5) in the wild, you wouldnt know if it was a complex number or just a 2 dimensional vector until it is operated upon.
  - ttoinou 8y ago
    The OP was looking for "explanation of complex numbers" You won't explain anything by talking about 2D points only But you can if you specify only how they behave with addition and multiplication (see my others posts)
    - enriquto 8y ago
      > The OP was looking for "explanation of complex numbers" > You won't explain anything by talking about 2D points only The OP was complaining about the explanation that complex numbers "have a real and an imaginary part", because it mean nothing to them. It is alright, then, to clarify that this just means that they are points in the plane, and some operations will be defined on these points.
      - ttoinou 8y ago
        Yes
darkscape 8y ago
Hmm, I tend to think that what one can do with some objects is an essential part of what they are. Two-dimensional vectors can just as well be thought of as points in the plane. What sets complex numbers apart is eg that we define complex multiplication of them. A more general example: a group is not just some set G, but that set with a binary operation satisfying certain axioms.