Also called absolute complement set, that is, generally speaking, let S be a set, A be a subset of S, and the set of all elements in S that do not belong to A is called absolute complement set of subset A in S.
The concept of supplement can be found online or read books. Many mathematical objects, such as numbers, functions and geometry, reflect the internal structure of continuous operations or the relationships defined in them. Mathematics studies the properties of these structures, for example, number theory studies how integers are represented under arithmetic operations.
In addition, things with similar properties often occur in different structures, which makes it possible for a class of structures to describe their state through further abstraction and then axioms. What needs to be studied is to find out the structures that satisfy these axioms among all structures.
Therefore, we can learn abstract systems such as groups, rings and domains. These studies (structures defined by algebraic operations) can form the field of abstract algebra.
Because abstract algebra has great universality, it can often be applied to some seemingly unrelated problems. For example, some ancient problems of drawing rulers and rulers were finally solved by Galois theory, which involved domain theory and group theory.
Another example of algebraic theory is linear algebra, which makes a general study of vector spaces with quantitative and directional elements. These phenomena show that geometry and algebra, which were originally considered irrelevant, actually have a strong correlation. Combinatorial mathematics studies the method of enumerating several objects satisfying a given structure.
The study of space originated from Euclidean geometry. Trigonometry combines space and numbers, including the famous Pythagorean theorem, trigonometric function and so on. Now the research on space has been extended to high-dimensional geometry, non-Euclidean geometry, topology and graph theory.
Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold.
Algebraic geometry has the description of geometric objects such as polynomial equation solution set, which combines the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change.