User:Lambiam/Mdefs
Mathematics can be defined as the logically rigorous study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions.
Mathematics is the study of topics such as quantity, structure, space, and change, using logically rigorous methods. This means that mathematical results can be justified by deductive reasoning, starting from axioms and definitions. Using this, a large body of knowledge has been created over the course of many centuries that is constantly expanded, covering many fields and comprising definitions, theorems, methods, and techniques, all of which build upon each other.
Mathematics is a discipline that studies topics including quantity, structure, space, and change. Its methodology emphasizes deductions made in logically rigorous fashion from axioms and definitions. Some mathematicians of a formalist bent consider this methodology actually to define mathematics, whereas those of a more realist viewpoint tend to find such a definition overly restrictive.
Mathematics is a discipline that studies topics including quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Its methodology emphasizes deductions made in logically rigorous fashion from axioms and definitions."
Mathematics is a discipline that studies topics including quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Using deductive reasoning, starting from axioms and definitions, a large body of knowledge has been created over the course of many centuries that is constantly expanded, covering many fields and comprising definitions, theorems, methods, and techniques, all of which build upon each other.
Mathematics is a discipline that studies topics including quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. While, guided by physical and mathematical intuition, its methodology emphasizes deductions made in logically rigorous fashion from axioms and definitions. It represents a large, constantly expanding body of knowledge, built up one idea upon another, over the course of many centuries."
Mathematics is a discipline that studies topics such as quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Over the course of many centuries a large body of knowledge has been created, covering many fields and comprising definitions, theorems, methods, and techniques, all of which build upon each other. Mathematicians justify their results mainly by deductive reasoning, starting from axioms and definitions.
Mathematics is a discipline that studies topics such as quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. It involves choosing appropriate axioms and definitions, and using deductive reasoning to prove theorems from these. In this way, over the course of centuries, a large constantly expanding body of knowledge has developed, covering a broad range of topics.
Mathematics is the discipline that studies topics such as quantity, structure, and space, and how they change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. It involves choosing appropriate axioms and definitions, and applying deductive reasoning to establish conjectured results concerning them; it also involves the application of those results to the physical world via modeling. Today mathematics covers an impressively broad range of topics.
Mathematics is a discipline that studies topics such as quantity, structure, space, and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. It involves choosing appropriate axioms and definitions, and using deductive reasoning to prove theorems from these. In this way, a large constantly expanding body of knowledge has developed, covering a broad range of topics.
Mathematics is a discipline that studies topics such as quantity, structure, space, change, and chance. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, the shapes and motions of physical objects, and outcomes of games. The method of mathematics is deductive reasoning from carefully stated axioms and definitions.
Mathematics is a discipline that studies topics including quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.
Mathematics is a discipline that studies topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.
Mathematics is a discipline that encompasses topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians prefer to prove results by rigorous deduction from axioms and definitions.
Mathematics is the study of topics such as quantity, structure, space, and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.
Mathematics is a discipline encompassing topics such as quantity, structure, space and change. It evolved, through the use of abstraction and logical reasoning, from counting, calculation, measurement and the study of the shapes and motions of physical objects. Mathematicians aim to justify their results by rigorous deduction from axioms and definitions.