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What is the basic idea of mathematics?
The basic ideas about mathematics are as follows:

Mathematical abstract thinking includes classified thinking, set thinking, combination of numbers and shapes, symbolic expression thinking, symmetrical thinking, corresponding thinking, finite and infinite thinking, etc.

Mathematical reasoning thinking includes inductive thinking, deductive thinking, axiomatic thinking, transformation thinking, analogy thinking, gradual approximation thinking, substitution thinking, special general thinking and so on.

Mathematical modeling ideas include simplification, quantification, function, equation, optimization, randomness and sampling statistics.

Mathematical thoughts include: the thought of function equation; The combination of numbers and shapes; Discuss ideas by category; Equation thought; Overall thought; Turn to thought; Implicit conditional thinking; Analogical thinking; Modeling ideas; Inductive reasoning thought; Extreme thoughts. Function thought refers to analyzing, reforming and solving problems with the concept and nature of function.

The idea of equation is to start with the quantitative relationship of the problem, transform the conditions in the problem into mathematical models (equations, inequalities or mixed groups of equations and inequalities) with mathematical language, and then solve the problem by solving equations (groups) or inequalities (groups).

Sometimes, functions and equations need to be transformed and interrelated to achieve the purpose of solving problems. Descartes' equation thought is: practical problem → mathematical problem → algebraic problem → equation problem. The universe is full of equality and inequality.

We know that where there are equations, there are equations; Where there is a formula, there is an equation; The evaluation problem is realized by solving equations ... and so on; The inequality problem is also closely related to the fact that the equation is a close relative. Column equation, solving equation and studying the characteristics of equation are all important considerations when applying the idea of equation.

"Numbers are invisible, not intuitive, and numerous shapes make it difficult to be nuanced", and the application of "combination of numbers and shapes" can make the problem to be studied difficult and simple. Combining algebra with geometry, such as solving geometric problems by algebraic method and solving algebraic problems by geometric method, is the most commonly used method in analytic geometry.

For example, find the root number ((A- 1)2+(B- 1)2)+ root number (A 2+(B- 1)2)+ root number ((A- 1) 2+B).