Reflexivity: let C={(x, y)|x, y belong to A}, let d be a nonempty set of c, if (x, y) belongs to d, it is said that x and y are related (designated by d) and marked as x ~ y (symbols (*, *) indicate their ordered pairs). If (x, x) belongs to D, the relationship specified by D is reflexive.

Symmetry: Mathematically, symmetry is expressed by group theory. Groups correspond to Galileo group, Lorenz group and U( 1) group respectively. The cases where symmetric groups are continuous groups and discrete groups are called continuous symmetry and discrete symmetry respectively.

Transitivity is in logic and mathematics. If A, B and C all belong to X, then the binary relation R on set X is transitive. If the following statement is still valid: "If A involves B and B involves C, A involves C .."

Symmetric operation

When a molecule has a center of symmetry, a straight line is connected from any atom in the molecule to the center of symmetry, and a second straight line is extended, so that another same atom can be found on the other side equidistant from the center of symmetry, and every point is symmetrical about the center. Symmetry operation according to the center of symmetry is inversion operation, and it is inversion according to the center of symmetry, which is denoted as I; In=E when n is even, and in=i when n is odd.

The basic operation of the anti-axis In is to rotate 360/n around the axis, and then the inversion is carried out according to the center point on the axis, followed by the joint operation of C 1n and I: I1n = IC1n; Rotate 360/n around the In axis, and then reverse according to the center.

Baidu encyclopedia-symmetry