PROOF PROCEDURE Meaning and
Definition
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A proof procedure refers to a systematic and methodical process employed in mathematics or logic to establish the validity or correctness of a given statement or theorem. It involves a series of logical steps or manipulations performed on a set of premises or axioms to derive or establish a conclusion. The primary objective of a proof procedure is to demonstrate the truthfulness or provability of a mathematical proposition.
In general, proof procedures often comprise a set of rules or principles that allow for the step-by-step transformation of statements, taking into account the logical relationships and connections between different mathematical concepts. These procedures often rely on the principles of deduction and inference, applying logical operations such as modus ponens, modus tollens, or transitivity to establish the validity of a theorem or proposition.
Proof procedures can vary depending on the specific field of mathematics or logic they are employed in. For example, in formal systems such as first-order logic, proof procedures may involve the use of axioms, rules of inference, and techniques such as natural deduction or sequent calculus. In other areas such as algebra or geometry, proof procedures may be centered around properties of numbers or geometric figures, respectively.
Through the use of proof procedures, mathematicians can demonstrate the rigor and validity of their mathematical arguments, ensuring that the conclusions reached are based on sound reasoning and logical principles. Proof procedures play a pivotal role in the development and advancement of mathematics and are essential for establishing new theorems and extending mathematical knowledge.
Etymology of PROOF PROCEDURE
The etymology of the word "proof procedure" is derived from the combination of two words: "proof" and "procedure".
- "Proof" originated from the Old French word "prove" meaning "evidence" or "proof". It further comes from the Latin word "proba" meaning "a test" or "proof". The term has its roots in the Proto-Indo-European word "pro-bhwo" meaning "to be good" or "to make good".
- "Procedure" comes from the Latin word "procedere", which can be broken down into "pro" meaning "forward" and "cedere" meaning "to go". It originally referred to the act of moving forward or advancing.
When combined, "proof procedure" refers to a systematic method or process used to ascertain evidence or establish the validity of a statement or claim.
