3 ms·

i is a complex number, complex numbers are of the form real + i*real... Don't you see the recursive definition ? Same with 0 and 1 they are not numbers until yo

by ttoinou 8mo ago

i is a complex number, complex numbers are of the form real + i*real... Don't you see the recursive definition ? Same with 0 and 1 they are not numbers until you can actually define numbers, using 0 and 1 i*i=-1 makes perfect sense This is one definition of i. Or you could geometrically say i is the orthogonal unit vector in the (real,real) plane where you define multiplication as multiplying length and adding angles

chongli 8mo ago
There's no issue with recursive definitions. That's how arithmetic was original formalized by Peano's axioms [1]. [1] https://en.wikipedia.org/wiki/Peano_axioms https://en.wikipedia.org/wiki/Peano_axioms
- ttoinou 8mo ago
  i is also a quaternion. So by this logic we could say complex numbers are made up of quaternions. But we don’t say such things because they wouldn’t be a good mental model of what we want to talk about.
  - srean 8mo ago
    > i is also a quaternion Yeah, so ? The fraction 1/2 is a rational and also a real and also a complex numbers and also a quaternion also an octonion .... We use a number along with the minimal abstraction that is sufficient for our purpose.
    - ttoinou 8mo ago
      i=0+1*i =0+1*(0+1*(0+1*(0+1*(0+1*(0+1*( ...*
      - deleted 8mo ago
        [deleted]
      - chongli 8mo ago
        ... = -2 - (-3) = -1 - (-2) = 0 - (-1) = 1 - 0 = 1 = 2 - 1 = 3 - 2 = 4 - 3 = 5 - 4 = ...