1, the polynomial about x, the highest degree is odd.

When x →∞, y →∞, so there is at least one real number root.

2. The principle of root-piercing method. The highest odd degree has at least one real root.

3. The so-called odd degree means that the degree of the x highest term of an equation or function is odd. The so-called even degree means that the degree of the x highest term of an equation or function is even.

The highest number of unknowns of a unary algebraic expression function or equation is the number of functions or equations, which is odd, that is, odd; Even numbers are even numbers. Odd equations have at least 1 real roots, and even equations may have no real roots.

Infinity in extended data mathematics

The symbol of infinity is that its Unicode is u+221e "∞" infinity, which is expressed as \ infinity in LaTeX.

1655 john wallis first used infinite symbols. After they are used, they are also used in fields other than mathematics, such as modern mysticism and semiotics.

Geometry and topology

Principal term: the dimension of vector space

Infinite dimensional space is often used in geometry and topology, especially classification space, that is, Eilenberg? Common examples of MacLane space are infinite dimensional complex projective space K(Z, 2) and infinite dimensional real projective space K(Z/2Z, 1).

Irregular fragment shape

The fractal structure can be enlarged repeatedly, and the fractal can be infinitely enlarged, but it will not become smooth and still maintain its original structure. The perimeter of fractal is infinite, some areas are infinite, but some areas are finite. For example, the Koch curve is an example of infinite perimeter and limited area.

There is no infinite mathematics.

Leopold Kronecker doubted the concept of infinity, and also doubted that mathematicians used infinite methods in 1960s and 1960s. This skepticism forms a mathematical philosophy called finitism, which belongs to an extreme form of mathematical structuralism and mathematical intuitionism.

reference data

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