Real numbers can compare sizes, but people who have studied complex numbers will find that we can't compare the sizes of two complex numbers, and we don't even know which imaginary unit "I" or "0" is bigger.
Any two numbers in the number field should be larger. First of all, the number field is an ordered field, that is, we can establish a set of rules to make all the numbers in the number field form an ordered relationship and be compatible in addition and multiplication.
Mathematically, for a number field Q, if a total order relation can be defined to make Q an ordered field, then the following two conditions must be met (A, B and C belong to Q):
Condition 1: when a>b has a+c > b+ c；
Condition 2: When a>b and c>0 have ac> in 200 BC.
For integer and real number fields, these two conditions are obviously satisfied, so both integers and real numbers are ordered fields, and any two elements of them can be compared in size.
Complex number is an extension of real number, and the imaginary unit "I" is introduced. We can regard the complex number field as a two-dimensional number, but no matter how it is defined, it cannot make the complex number meet the two conditions of the ordered field.