There are three representations of domain: inequality, interval and set.

The domain of y=[√(3-x)]/[lg(x- 1)] can be expressed as:1) x ≤1; 2)x∈(-∞， 1]； 3){x|x≤ 1}. Let a and b be two groups of non-empty numbers. If we follow a certain correspondence F, there will be a unique number f(x) corresponding to any number X in set A;

Then we call f: a-b a function from set A to set B, and we call it y=f(x), and x belongs to set A, where x is called an independent variable and its range A is called the domain of the function.

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Introduce inequality

Inequality is a formula connected by an inequality symbol. Inequalities are divided into strict inequalities and non-strict inequalities. Inequalities connected by pure greater than sign and less than sign are called strict inequalities, while inequalities connected by not less than sign (greater than or equal to sign) and not greater than sign (less than or equal to sign) are called non-strict inequalities or generalized inequalities.

Interval introduction

An interval is a set of numbers within a certain range, which is generally expressed in the form of a set. As the simplest set of real numbers, interval plays an important role in integral theory. Interval arithmetic is a numerical analysis method used to calculate rounding error.

Brief introduction of sets

Set is a basic mathematical concept and the research object of set theory. Refers to the sum of things with certain properties, and the things in the set are called elements. A modern set is usually defined as a whole consisting of one or more definite elements.

Set has unparalleled special importance in the field of mathematics. The foundation of set theory was laid by German mathematician Cantor in the 1970s of 19. After the efforts of a large number of scientists for half a century, it established its basic position in the modern mathematical theory system in the 1920s. It can be said that the achievements of all branches of modern mathematics are almost based on strict set theory.