Limit of dialectical thinking thinking

Abstract: Limit theory throughout the calculus, calculus is an important and difficult. Recognized limits to grasp and understand the limits of thought is the premise of the theory through the philosophy of dialectical thought and limit close contact to strengthen the ideological limits of the dialectical understanding, help in mathematical thinking and mathematical literacy training to improve.

Keywords: limit thinking, dialectical philosophy, the unity of opposites
0 Introduction.

Calculus is the study of the phenomenon of the objective world sport, a discipline, we introduce the concept of limit movement of the objective world to be described, with the limit method to establish the relationship between the number of results and to study its motion [1] the limit theory is the basic theory of calculus throughout the whole calculus. to learn calculus, we must recognize and understand the limits of theory, and theory to grasp the limits of the premise, we must first understand the ideological limits. extreme ideology contains rich dialectical thought, is to change and the process and results , finite and infinite, is approximately accurate, quantitative and qualitative change and negation and affirmation of the unity of opposites.

A limit of thought and dialectical philosophy links.

1.1 limit idea is to change and the unity of opposites.

"Change" and "change" reflects the objective movement of things change in two different states with relatively static, the same is relative, change is absolute, but they can be transformed into each other under certain conditions, for example, a plane curve C P is a point on the tangent slope of kp. In addition to points on the curve point P outside the slope k is variable, kp is variable, different points on the curve corresponding to different slope K, the slope k can not be equal to kp, k and kp is to change and the antagonistic relationship, while between them, also reflects a relationship of mutual interdependence contact when infinitely close points on the curve point P process, the slope k infinitely close to kp, the same amount of change amount approaching when the result of infinitely close to a qualitative leap forward, the variable transformed into invariant, that is "change" and "change", which reflects the unity between the changed and unchanged.

1.2 limit idea is to process and outcome of the unity of opposites.

Process and results in philosophy is a dialectical relationship between unity in the limit of thought but also fully embodies the unity of opposites and the process results in the above example, when the point on the curve near the point P of the infinite process of change, k is the process of change , kp is the result of changes in the one hand, no matter how close to the point on the curve point P, can not coincide with the point P, the same point on the curve changes the slope of k is not equal to kp, which reflects the process and results of the confrontation, the other , along with the infinitely close to the process, closer to the slope k kp, there are close links between the two, infinitely close to the result of the changes made into the slope k kp, which reflects the unity of the process and result, so by the slope of the curve point P k of the change process to get the slope of kp is the point of the process and results of the unity of opposites.

1.3 limit idea is finite and the infinite unity of opposites.

In the dialectical method, the finite and the limit is the unity of opposites. Unlimited and limited essentially different, but both have contact, unlimited is limited development, but with the limit law, from the limited understanding of the infinite [2] For example, in limit-type lim n → ∞ xn = a in xn the corresponding series in each of these different values ​​xn both the relatively static nature, but also the absolute mobility. series in each of the xn and a are determined not the amount of change is a finite number as n increases infinitely, a limited number of xn to tap into a infinite, it is these changes in a limited number of xn infinite, infinite movement reflects the process of change, this movement changes the result is an infinite number Thus in the limit of infinite thought is limited development, the result of the limited is unlimited, they are both antagonistic and unified.

1.4 limit is approximate and exact thought the unity of opposites.

Approximate and exact relationship between the unity of opposites, under certain conditions, can be transformed into each other, this transformation is an important way to understand mathematics [2].

In the limit of an abstract concept, the introduction of examples such as "inscribed regular polygon area", within the polygon area is the junction area of ​​a circle approximation, when the infinite number of edges of polygons increases, the deformation within the area of ​​multi-junction area of ​​infinitely close to the circle , obtained after taking the limit area of ​​a circle the exact value, which is the limit with the law, from the approximate knowledge accurate. Another example is type in the limit lim n → ∞ xn = a, when n increases infinitely, the series of items x1, x2, ..., xn xn infinitely variable to reflect the change process, and a reflection of changes in the results of infinite variables xn, xn is a approximation of each, and when n is greater the higher the accuracy when n tends to infinity , xn into an accurate approximation of the value of a. Although the approximate nature and precision are two different, mutually exclusive concepts, but by the limit law, to establish the link between the two, under certain conditions, can be transformed into each other, so both approximate and exact opposition is united. Links to free download http://www.hi138.com 1.5 idea is to limit the quantitative and qualitative change in the unity of opposites.

In the materialist dialectics, everything has a qualitative and quantitative, are the quality and quantity of the entity. Quality is a thing into its own and different from other things, internal regulations, the amount refers to the existence of scale , level of development and speed, and its composition in the space of permutations and combinations, etc. can be used to indicate the number of the provisions of [3] both quantitative and qualitative differences there are links between the two has a dialectical relationship is a quantitative qualitative change in preparation, the amount of change reaches a certain degree, inevitably lead to a qualitative change, qualitative change is the only fundamental change in the nature of things, a qualitative change in the law of quantitative research in mathematics play an important role [4] for any one unit circle inscribed regular polygon, quality of things is round inscribed polygon, then the amount is within the polygon edges, when the number of edges in an infinite increase in obtained is still inscribed regular polygon, is quantitative, not qualitative, quantitative expression the continuity of the development of things in the process of quantitative change things, to maintain quality of the stability of the thing itself, but when increasing the number of edges of the infinite process, due to the amount of dynamic change, getting closer and closer round the polygon, create the conditions for the qualitative change, polygon area to change into a circular area, the amount of quality to promote the transformation to achieve unification of contradictions.

1.6 limit is negative and positive thinking the unity of opposites.

Anything internally contains positive elements and negative factors are positive aspects and negative aspects of the unity of opposites. Unit circle and its inscribed regular polygon are two opposite things, is a regular polygon inscribed things on their own sure, which also includes the negative, this negative factor is the inner circle inscribed regular polygon edges by the change reflected in the number of As inscribed regular polygon edges gradually increased to infinity, the internal area of ​​the polygon the unit circle into the area, prompting the things into their own opposites, by the almost certainly be its own negation, which reflects the negative and positive opposition, round and round the inscribed regular polygon, although the two opposites, but There are close links between the two, inscribed regular polygon of the area can be transformed into area of ​​a circle, and gradually increase the unit circle is inscribed regular polygon edges to achieve in order to establish this link between the two, reflects the negative and positive unity.

2 limit thought and dialectical philosophy of meaning.

In dialectical materialism, the interaction between objective things, the relationship between constraints and interaction everywhere, even in completely different in nature, the two contradictory things, but also has its side of each other, so in the calculus The learning process can not be ignored the ideological penetration of dialectical materialism in general. dialectical thinking in mathematical thinking and understanding of the penetration, its essence is in accordance with the principles of dialectical materialism in the development of contacts and knowledge to grasp the object, in the unity of opposites in the understanding of things Through the above analysis, the ideological limits of the scope of philosophy throughout the materialist dialectic, which reveals the variable and constant process and results, finite and infinite, is approximately accurate, quantitative and qualitative change in the unity of opposites [4], when we understand the limits of thought must be single, closed, static form of logical thinking to multi-dimensional, open, static and dynamic combination of dialectical thinking. mathematical thinking and philosophy is the integration of high-level requirements to learn math, and understand mathematical thinking in philosophy and in philosophy under the guidance of mathematical thinking, is to improve students' mathematical literacy, understanding of mathematical knowledge, mathematical ability of students in important ways and means [5].

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References:
[1] Shen Chang-hua: <<Calculus development of the concept and philosophy resolved>> [D], <<Lanzhou University, a master's degree thesis>> 2007:10-15.

[2] Wuzhen Ying, Chen Zhan this: <<On the limits of thinking>> [J], <<Journal of Guangzhou University>> 2003 (10:410-412.

[3] Juan: <<calculus teaching philosophy penetration>> [J], <<Higher Correspondence>> 2007 (12:8-10.

[4] Bai Shuzhen: <<dialectical understanding of the limits of thinking>> [J], <<China-school education>> 2008 (02:39-40.

[5] Sun Wei, Bai Suying: <<Calculus teaching function of Philosophy>> [J], <<Harbin Finance College>> 2005 (3:55-56. Links to free download http://www.hi138.com