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Reasoning is the basic thinking of mathematics. What kind of reasoning does reasoning generally include?
1, deductive reasoning

Deductive reasoning is a reasoning method from general to special. Contrary to induction. The connection between reasoning premise and conclusion is inevitable, and it is a kind of conclusive reasoning.

Using this method to study problems, we must first correctly grasp the general principles and principles as guiding ideology or basis; Secondly, we should fully understand the actual situation and particularity of the topics and problems to be studied; Then we can deduce the conclusion that general principles are applied to specific things.

Including syllogism, hypothetical reasoning and selective reasoning. In educational work, it is essential to design and carry out educational and teaching experiments according to certain scientific principles.

2. Inductive reasoning

Inductive reasoning is a kind of reasoning from individual to general. From a certain point of view about individual things to a larger point of view, the general principle and the explanation method of the principle are deduced from special concrete examples.

What is in nature and society generally exists in the individual and the special, and exists through the individual. Generally exists in specific objects and phenomena. Therefore, only by knowing the individual can we know the general.

Extended data

Inductive reasoning is inseparable from deductive reasoning. First, in order to improve the reliability of inductive reasoning, it is necessary to use the existing theoretical knowledge to analyze the individual premise of inductive reasoning and grasp the causality and inevitability, which requires deductive reasoning.

Secondly, inductive reasoning relies on deductive reasoning to verify its own conclusions. For example, Russian chemist Mendeleev discovered the periodic law of elements through induction, and pointed out that the properties of elements change periodically with the increase of atomic weight of elements.

Later, through deductive reasoning, it was found that the atomic weights of some elements originally measured were wrong. So he rearranged their positions in the periodic table, predicted some undiscovered elements, and pointed out that blank positions should be reserved for new undiscovered elements in the periodic table.

Baidu encyclopedia-deductive reasoning

Baidu encyclopedia-inductive reasoning