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List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.
Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth ...
Mathematical induction is an inference rule used in formal proofs, and is the foundation of most correctness proofs for computer programs. [ 3 ] Despite its name, mathematical induction differs fundamentally from inductive reasoning as used in philosophy , in which the examination of many cases results in a probable conclusion.
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems ; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms ...
Proof theory is a major branch [1] of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed ...
3 Other axioms of mathematical logic. 4 Geometry. 5 Other axioms. 6 See also. Toggle the table of contents. List of axioms. 3 languages.
The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, parts of computer science. Subsequent discoveries in the 20th century then stabilized the foundations of ...
These proofs of the Fundamental Theorem of Algebra must make use of the following two facts about real numbers that are not algebraic but require only a small amount of analysis (more precisely, the intermediate value theorem in both cases):