AXIOM SCHEME Meaning and
Definition
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An axiom scheme refers to a fundamental, foundational principle or proposition in mathematics or logic that serves as a starting point for deriving theories or proving statements. It represents a collection or set of axioms, which are self-evident truths or postulates that do not require proof themselves. However, the axiom scheme as a whole, rather than individual axioms within it, provides the basis for reasoning and inference in mathematical or logical systems.
The term "scheme" in axiom scheme indicates that it encompasses multiple axioms that are related or interconnected. This distinguishes it from a single, isolated axiom. The set of axioms within an axiom scheme are typically selected to capture essential and universal truths necessary to build a coherent and consistent mathematical or logical framework.
The purpose of an axiom scheme is to establish a solid foundation upon which further mathematical or logical conclusions can be built. By accepting the truth of the axioms within the scheme, mathematicians or logicians can establish the validity of various theorems or proofs. Axiom schemes are often utilized within formal systems like set theory, number theory, or predicate logic.
In summary, an axiom scheme is a collection of self-evident principles that serve as the starting point for mathematical or logical reasoning. It provides a set of foundational truths upon which theorems and proofs can be constructed, forming the basis for rigorous mathematical or logical investigations.
Etymology of AXIOM SCHEME
The word "axiom" originates from the Greek word "axios", meaning "worthy" or "excellent". It entered the English language around the 15th century through Latin, where it was used to refer to a self-evident truth or principle that required no proof. The term "scheme", on the other hand, traces its roots back to the Old Norse and Old English words "skeitha" and "sceamian", respectively, both meaning "a plan or design".
When combined, "axiom scheme" typically refers to a set of axioms or principles that form the foundation or framework for a particular theory, system, or field of study. Although these terms have different linguistic origins, their combination describes a concept in formal logic and mathematics.
