“i” is not a Constant¶
People will sometimes call
together with numbers like
This is a misunderstanding of the concept.
A constant is something that has a definition
from the abstract field.
For example, you can define
“take a complete ordered field,
and find the least upper bound of
for all natural numbers
It does not matter how the real numbers are represented: cauchy sequences or Eudoxus reals, it’s all the same. The least upper bound is unique, and points to a specific element in the field.
this is not true for
“In the unique algebraic completion
of a complete ordered field,
the number that,
is equal to
does not identify
Indeed, there is no theoretical way to identify
Complex number conjugation
is a continuous automorphism of the complex number field,
so there is no property
does not share.
The real number field has no non-trivial automorphisms,
so this problem is unique to
If you need a complex constant,
you can indicate the real and imaginary parts,
both of them real numbers,
and the only