Briefly introduce inductive reasoning and analogical reasoning, and give an example.

Inductive reasoning inductive reasoning refers to the reasoning that different objects of a certain kind of things have certain characteristics, and all objects of this kind of things have these characteristics. It is reasoning from the part to the whole, from the special to the general.

Example: Calculate and observe the following formulas: 8×8=64, 5×5=25,12×144, 7×9 =63, 4×6=24,1/kloc. It is known that 25×25=625, then? 26×24= ?

In the teaching process of "polygon interior angle theorem", the teacher raised such a question: "Who can tell me the sum of the interior angles of a quadrilateral?"

Student: "The sum of the internal angles of a quadrilateral is 360".

Teacher: "What is the sum of the internal angles of a Pentagon? How about a hexagon? ……"?

Students will have some questions, and then the teacher will guide them to sum up.

Analogical reasoning Analogical reasoning is based on the fact that two or two objects have some same or similar properties, so as to infer that their other properties are also the same or similar.

For example, learning solid geometry is similar to plane geometry. When studying spheres, spheres and circles are similar in shape. They are all point sets whose distance to a fixed point is equal to a fixed length. A circle has a tangent, and the tangent intersects the circle at only one point. The distance from the tangent point to the center of the circle is equal to the radius of the circle.

Inductive reasoning and analogical reasoning are based on the existing facts, after observation, analysis, comparison, association, induction and analogy, and then conjectural reasoning is put forward, which we collectively call reasonable reasoning.

The conclusions drawn by the two men are not necessarily correct and need further proof.

analogism

Different from inductive reasoning, analogical reasoning is more imaginative and creative than inductive reasoning.

Inductive reasoning?

The conclusion of inductive reasoning is speculative, and the truth of the conclusion needs to be proved by logic and practice. So it can't be used as a tool for mathematical proof.

Inductive reasoning is a kind of creative reasoning. The conjecture obtained by inductive reasoning can be used as the starting point for further research, helping people find problems and ask questions.