Conventional time is modelled as the one dimensional continuum R^1 of real numbers. This continuity, however, does { \em not} stem from { \em any} fundamental principle. On the other hand, natural time is { \em not} continuous and its values as well as those of the energy, form { \em countable} sets, i.e., with cardinalities either finite or equal to \aleph_0, where this symbol stands for the { \em transfinite} number of natural numbers. For infinitely large number of events, the values of natural time form a { \em denumerable} set, i.e., its cardinality is exactly \aleph_0, while those of conventional time an { \em uncountable} set. This has a drastically larger cardinality, which in the light of the continuum hypothesis becomes equal to 2^{ \aleph_0}.
Categories: cond-mat.other