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The choice of the "shortest tree" relative to a not-so-short tree under any optimality criterion (smallest distance, fewest steps, or maximum likelihood) is always based on parsimony. [61] Francis Crick has commented on potential limitations of Occam's razor in biology. He advances the argument that because biological systems are the products ...
They disagree on how important self-organization is in other areas of biology. The mathematical biologist Stuart Kauffman suggested in 1993 that self-organization may play a role alongside natural selection in three areas of evolutionary biology, namely population dynamics, molecular evolution, and morphogenesis.
All theorems and corollaries are proven by exploring the implications of the axiomata and other theorems that have previously been developed. New terms are defined using the primitive terms and other derived definitions based on those primitive terms. In a deductive system, one can correctly use the term "proof", as applying to a theorem.
The mathematical statements discussed below are provably independent of ZFC (the canonical axiomatic set theory of contemporary mathematics, consisting of the Zermelo–Fraenkel axioms plus the axiom of choice), assuming that ZFC is consistent. A statement is independent of ZFC (sometimes phrased "undecidable in ZFC") if it can neither be ...
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
Biology portal; Pages in category "Biological theorems" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. B. Bet ...
Many theorems provable using choice are of an elegant general character: the cardinalities of any two sets are comparable, every nontrivial ring with unity has a maximal ideal, every vector space has a basis, every connected graph has a spanning tree, and every product of compact spaces is compact, among many others. Frequently, the axiom of ...
The summation theorem suggests this does not necessarily have to be the case. The flux summation theorem also suggests that there is a total amount of flux control in a pathway such that if one step gains control another step most lose control. Plot of a phenotype, such as a flux, as a function of enzyme level.