Standard mathematical economics studies the production, exchange, and consumption of goods “
However, economics, and many other domains of life sciences, investigate also what will be called
(1) Denoting by $X$ the set of entities $x \in X$
(2) Entities can be “gathered” instead of being “added”;
(3) Entities can still be evaluated by a
(4) Subsets of entities can be evaluated by an “
Life sciences dealing with intertwined relations among many combinations of entities, hypersets offer metaphors of “Lamarckian complexity” that keeps us away from binary relations, graphs of functions, and set-valued maps, to focus our attention on “
This is the object of this
We no longer have to add goods which can only be gathered, prices do not have to be linear, although it costs some effort to deprive oneself of the powerful and luxurious charms of convex and linear functional analysis motivated by physics.
These sacrifices concern only economics and other fields of life science, since physicists deal with experimental observations of objects endowed with unit of measurement by adequate processes of measurement. They can happily live in vector spaces without any guilt. This is not the case of life scientists, who have mainly history to support and validate their observations, with, sometimes, the privilege to statistically measure the frequency of some of them.
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