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  2. Models of scientific inquiry - Wikipedia

    en.wikipedia.org/wiki/Models_of_scientific_inquiry

    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.

  3. Category:Biological theorems - Wikipedia

    en.wikipedia.org/wiki/Category:Biological_theorems

    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 ...

  4. List of statements independent of ZFC - Wikipedia

    en.wikipedia.org/wiki/List_of_statements...

    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 ...

  5. Mathematical and theoretical biology - Wikipedia

    en.wikipedia.org/wiki/Mathematical_and...

    Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...

  6. Axiom of choice - Wikipedia

    en.wikipedia.org/wiki/Axiom_of_choice

    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 ...

  7. Immersion (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Immersion_(mathematics)

    For infinite dimensional manifolds, this is sometimes taken to be the definition of an immersion. [4] An injectively immersed submanifold that is not an embedding. If M is compact, an injective immersion is an embedding, but if M is not compact then injective immersions need not be embeddings; compare to continuous bijections versus homeomorphisms.

  8. Structural biology - Wikipedia

    en.wikipedia.org/wiki/Structural_biology

    With the development of these three techniques, the field of structural biology expanded and also became a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of biological macromolecules (especially proteins, made up of amino acids, RNA or DNA, made up of nucleotides, and membranes, made up of ...

  9. Structuralism (biology) - Wikipedia

    en.wikipedia.org/wiki/Structuralism_(biology)

    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.