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It is part of a broad class of indispensability arguments most commonly applied in the philosophy of mathematics, but which also includes arguments in the philosophy of language and ethics. [14] In the most general sense, indispensability arguments aim to support their conclusion based on the claim that the truth of the conclusion is ...
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
In mathematics and other fields, [a] a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem".
An argument is a set of premises together with a conclusion. [60] An inference is the process of reasoning from these premises to the conclusion. [43] But these terms are often used interchangeably in logic. Arguments are correct or incorrect depending on whether their premises support their conclusion.
Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. [1]