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Definitions from WordNet

Definitions from the Web

Metamathematics

Definition: Metamathematics is a branch of mathematics that focuses on the study of mathematical proofs and the foundations of mathematics itself.

Senses and Usages:

Sense 1: Study of Mathematical Proofs

Metamathematics involves the examination and analysis of mathematical proofs. It explores the structure, properties, and limitations of formal systems used in mathematics.

Sample Sentence 1: In metamathematics, researchers investigate the consistency and completeness of various axiomatic systems.

Sample Sentence 2: Metamathematics plays a crucial role in understanding the underlying logic and structure of mathematical arguments.

Sense 2: Foundations of Mathematics

Metamathematics delves into the foundations of mathematics, focusing on the philosophical and logical aspects of mathematical structures.

Sample Sentence 1: The study of metamathematics helps mathematicians inspect the assumptions and principles on which mathematical theories are built.

Sample Sentence 2: Metamathematics provides a framework for analyzing the theoretical foundations of arithmetic, set theory, and other mathematical branches.

Sense 3: Popular Usage

Metamathematics is occasionally used in a more informal sense to refer to any complex or abstract mathematical concepts that are difficult to comprehend.

Sample Sentence 1: The advanced calculus course was like metamathematics to me; it took several readings before I grasped the concepts.

Sample Sentence 2: Quantum mechanics can seem like metamathematics to many non-physicists due to its intricate mathematical formalism.

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