Bloch's Principle is a
philosophical principle in
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
stated by
André Bloch.
Bloch states the principle in Latin as: ''Nihil est in infinito quod non prius fuerit in finito,'' and explains this as follows: Every proposition in whose statement the
actual infinity occurs can be always considered a consequence, almost immediate, of a proposition where it does not occur, a proposition in ''finite terms''.
Bloch mainly applied this principle to the theory of
functions of a
complex variable. Thus, for example, according to this principle,
Picard's theorem corresponds to
Schottky's theorem, and
Valiron's theorem corresponds to
Bloch's theorem.
Based on his Principle, Bloch was able to predict or conjecture several
important results such as the
Ahlfors's Five Islands theorem,
Cartan's theorem on holomorphic curves omitting hyperplanes,
Hayman
Hayman is both a surname and a given name. Notable people with the name include:
Surname
*Al Hayman (1847–1917), business partner of Charles Frohman in ''Theatrical Syndicate''
*Andy Hayman, CBE, QPM (born 1959), retired British police officer, ...
's result that an exceptional set of radii is unavoidable in
Nevanlinna theory.
In the more recent times several general theorems were proved which can be regarded as rigorous statements in the spirit of the Bloch Principle:
Zalcman's lemma
A family
of functions
meromorphic on the unit disc
is not normal if and only if there exist:
* a number
* points