Why complex numbers cannot be compared

  • Can we compare real and complex numbers?

    Among any two integers or real numbers one is larger, another smaller.
    But you can't compare two complex numbers..

  • Can you compare a complex number to a real number?

    The answer is no In this video, I show that there is no way to compare the complex numbers in a way that 3 very natural properties are satisfied..

  • What makes complex numbers unique?

    The letter C represents the set of all complex numbers.
    C also forms a two-dimensional vector space.
    Unlike real numbers, complex numbers have no natural order.
    There are pure imaginary numbers, the real part of which is 0; their formula is as follows: 0 + bi = bi..

  • Why are complex numbers not comparable?

    TL;DR: The complex numbers are not an ordered field ; there is no ordering of the complex numbers that is compatible with addition and multiplication.
    If a structure is a field and has an ordering , two additional axioms need to hold for it to be an ordered field..

  • Why complex numbers Cannot be compared?

    Complex numbers are unordered.
    You cannot compare them.Jan 29, 2021.

  • Why complex numbers Cannot be ordered?

    Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
    Squares are necessarily non-negative in an ordered field.
    This implies that the complex numbers cannot be ordered since the square of the imaginary unit i is −1 (which is negative in any ordered field)..

  • Why we can t compare complex numbers?

    Complex numbers are unordered.
    You cannot compare them.Jan 29, 2021.

  • Complex numbers have the additional property, that ordinary vectors lack, that we can define multiplication among them so as to obey the usual commutative, associative and distributive laws of arithmetic.
  • The Complex Plane
    a is called the real part of the complex number, and b is called the imaginary part.
    Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.
    I.e., a+bi = c+di if and only if a = c, and b = d.
From my (programmer's) perspective, real numbers exist only in one dimension, while complex could be presented in two dimensions, hence no ordering comparison between both is possible (if we are not talking about modulus, which is a bit different).
The fact that complex numbers reside in a two-dimensional plane implies that inequality relations are undefined for complex numbers. This is a critical difference between complex and real numbers. But since complex numbers lie in a two-dimensional plane, they cannot be compared using “<” or “>”.
The fact that complex numbers reside in a two-dimensional plane implies that inequality relations are undefined for complex numbers. This is a critical difference between complex and real numbers. But since complex numbers lie in a two-dimensional plane, they cannot be compared using “<” or “>”.

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