ordinal reality

[AntonioLao]

By definition ordinal numbers possess the sole attribute of ‘order.’ This is the natural comparative idea of ‘greater than’ or ‘less than’ in addition to the idea of equality. If A and B are two ordinal numbers then the question whether A is greater than or less than or equal to B can be answered. Since both A and B can be mapped along the real number line and by inductive reasoning any real number has this property of orderliness, the one dimensionality of ordinal numbers can be definitely assured and well established.

However, the same cannot be said for higher dimensional numbers. By definition, the set of complex numbers has a higher cardinality than the set of real numbers. Moreover, complex numbers are two dimensional numbers since they are composed of a real part and an imaginary part and are located everywhere on the continuum of the complex plane. Given two complex numbers M and N, nothing can be said whether M is greater than or less than or equal to N unless their absolut values are defined as their complex moduli. Unfortunately, there are infinitely many complex numbers with the same complex modulus. Higher dimensional numbers called hypercomplex numbers like vectors, tensors, spinors, and many others also have no property of orderliness, the comparative attribute of ‘greater than’ or ‘less than’ or ‘equal to.’ This terse discussion asserts the absolute one dimensionality of ordinal reality.