Random strings were first studied by in the 1960s by A . N . Kolmogorov ( who had provided the first axiomatic definition of probability theory in 1933 ), Chaitin and Martin-L�f.
12.
All of it is deeply intertwined with an immoral, coercive state system . " By accepting an axiomatic definition of private property and property rights, anarcho-capitalists deny the legitimacy of a state on principle:
13.
This axiomatic definition of a Boolean algebra as a set and certain operations satisfying certain laws or axioms " by fiat " is entirely analogous to the abstract definitions of field etc . characteristic of modern or abstract algebra.
14.
Walther von Dyck ( 1882 ) introduced the idea of specifying a group by means of generators and relations, and was also the first to give an axiomatic definition of an " abstract group ", in the terminology of the time.
15.
The current standard axiomatic definition is that real numbers form the unique field up to an isomorphism, whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or infinite decimal representations, together with precise interpretations for the arithmetic operations and the order relation.
