Incomplete induction is a kind of reasoning method. By analyzing and summarizing some situations, a general conclusion is drawn. Incomplete induction also plays an important role in mathematical discovery. Incomplete induction can help mathematicians discover new mathematical concepts and theorems.
Mathematicians can find laws and trends by analyzing and summarizing known mathematical facts, and then put forward new mathematical concepts or theorems. For example, mathematicians summed up the definition and nature of arithmetic progression by observing and analyzing a series of arithmetic progression, and then extended it to a more general type of sequence.
Incomplete induction can help mathematicians find the internal relations between mathematical problems. Mathematicians can find their similarities and differences by summarizing and comparing problems in different mathematical fields, and then establish the relationship between mathematical theories. This method of induction and comparison can help mathematicians find new mathematical problems and open up new research fields.
Incomplete induction can also help mathematicians to test and prove mathematical theorems. In mathematical proof, induction is often used to prove some mathematical propositions. By reducing the problem to some basic sub-problems, and then solving these sub-problems one by one, the original proposition can be finally proved. For example, induction is often used in combinatorial mathematics to prove some problems.
The importance of incomplete induction;
1. Exploring new knowledge: Incomplete induction is of great significance in the process of exploring new knowledge. If people want to know the things around them, they should first make a lot of observations and experiments on the phenomena of things, and then use the incomplete induction from individual knowledge to general knowledge according to a series of individual facts confirmed by observations and experiments, so as to realize universal regularity.
2. Propose the hypothesis: In the specific investigation work, the investigation hypothesis plays an extremely important role. Because after the preliminary investigation of the scene of the case, in the face of complex situations, in order to reduce the blindness of investigation, we must rely on the investigation hypothesis to determine its investigation direction, so as to ensure that the investigation work is carried out in the right direction or track. The reasoning used at this time is mainly simple enumeration induction in incomplete reduction reasoning.