Reconstruction Of Real Number System With Decimal As Main Line

The understanding of number and the expansion of number system are the main mel ody and key of mathematics learning and theoretical construction.The construction of ha rmonious,unified and continuous real number system is the theoretical basis of differenti ability and integrability,and also the key to the horizontal and deep development of subje ct theory.The key to build a consistent real number system lies in the clear main line,in other words,the main line of "carrying out" the decimal.In the current textbooks,the basic idea for the construction of the real number syste m is around the two dimensions of fraction and decimal,that is,in the early stage,the rea l number system is gradually expanded with fraction as the center,and decimal is the "va ssal" of fraction.Rational number is defined by fraction,while decimal is in the side posi tion.In the last step of the real number system,irrational number is "pushed down and re built",and the real number system is defined with decimal as the center.According to thi s logic,the dimensions of the real number system are different,the relationship between f ractions and decimals is not well communicated,the fault of dimensions appears,and the main line of the whole real number system is fuzzy.At the same time’ the traditional idea of constructing real number system also brings some misunderstanding such as "the point on the number axis corresponds to the real number one by one".Based on this,this paper focuses on the topic of "measuring real numbers and recon structing real number system with decimals as the main line".Decimals are completely in dependent of fractions.Through measurement,"measuring" decimals is regarded as the "backbone" of real number system,and the whole real number system is directly defined b y decimals.As for the number with infinite square root and fraction,it is totally different from the traditional arrangement.It is regarded as the "branch" of the real number system.By establishing the equivalence between fraction and finite decimal or infinite circular d ecimal,it is an expression of irrational number that the number with infinite square root i s "long" to the decimal,which makes the real number system with decimal as the main li ne flourish.Finally,through the process of measuring decimals,the origin and positive hal f axis of the number axis are abstracted,and the negative real number system is derived a ccording to its reverse extension,so that the real number system corresponds to the point s on the line of the number axis one by one,and its continuity is realized.Under the guidance of this overall idea,this paper makes a concrete reconstruction p lan for the whole real number system of primary and secondary schools,including the ne w reconstruction of the knowledge points of decimal,fraction,open-ended number,negative number and number axis,so as to make the basic idea of "recons truction of real number system with decimal as the main line" take root,so as to have a n ew meaning for the theoretical construction and teaching application of real number syste m Breakthrough and reference.