MATHEMATICAL PROOF Meaning and
Definition
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Mathematical proof refers to a rigorous and systematic demonstration of the truth or validity of a mathematical statement or theorem. It provides a logical argument or evidence that establishes beyond doubt the accuracy of a mathematical claim.
In mathematics, a proof is constructed to convince others (and even oneself) that a particular statement is true, based on logical reasoning that follows established mathematical principles, axioms, definitions, and previously proven theorems. It involves a step-by-step presentation of interconnected ideas and logical deductions that lead from a set of assumed premises to the desired conclusion.
A mathematical proof must be clear, concise, and unambiguous, leaving no room for doubt or uncertainty. It typically employs symbols, equations, figures, and diagrams to illustrate and express the series of logical steps followed to establish the truth of the claim. A successful proof provides a convincing and irrefutable argument that all possible cases have been considered and that the conclusion holds universally.
Proofs play a fundamental role in mathematics, helping to ensure the accuracy and reliability of mathematical knowledge. They form the backbone of mathematical research, strengthening the foundation of theories, and providing robust evidence of their truth. Mathematical proofs also enable mathematicians to communicate their findings to the larger mathematical community, ensuring the integrity and trustworthiness of mathematical knowledge.
Common Misspellings for MATHEMATICAL PROOF
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Etymology of MATHEMATICAL PROOF
The word "mathematical" originates from the ancient Greek word "mathematikos", which means "related to learning, inclined to learn". This term came from "mathema", which refers to "science, knowledge". The word "proof" stems from the Old French word "preve" and Latin word "probare", both meaning "to test or demonstrate". "Probare" itself is derived from the Proto-Indo-European root "*pro-bhwo", meaning "good, strong". In the context of mathematics, a "proof" denotes a rigorous and logical demonstration that validates the truth or validity of a mathematical statement. Therefore, "mathematical proof" refers to a methodical and systematic confirmation of mathematical propositions.
Similar spelling words for MATHEMATICAL PROOF
