1. Mathematical induction: Through induction, general laws can be abstracted from several concrete examples, thus proving a theorem.
2. Mathematical reasoning: Prove the correctness of a theorem by proving its preconditions.
3. Mathematical reduction to absurdity: A theorem is proved to be incorrect by reduction to absurdity, thus proving the correctness of a theorem.
Data expansion:
Mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information.
Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.
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Mathematical language is also difficult for beginners. How to make these words have more accurate meanings than everyday language also puzzles beginners. For example, the words "open" and "domain" have special meanings in mathematics. Mathematical terms also include proper nouns such as embryo and integrability. But these special symbols and terms are used for a reason: mathematics needs accuracy more than everyday language. Mathematicians call this requirement for linguistic and logical accuracy "rigor".
Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. In this sense, mathematics belongs to formal science, not natural science. All mathematical objects are artificially defined in essence. They do not exist in nature, but only in human thinking and ideas.
Therefore, the correctness of mathematical propositions can not be tested by repeated experiments, observations or measurements, like physics, chemistry and other natural sciences whose purpose is to study natural phenomena, but can be directly proved by strict logical reasoning. Once the conclusion is proved by logical reasoning, then the conclusion is correct.