上确界的定义，你们开学了吗？

1from manim import *2import numpy as np3 4config.tex_template = TexTemplateLibrary.ctex5config.tex_template.add_to_preamble(r"\setCJKmainfont{STSong}")6 7class SupremumInfimum(Scene):8    def construct(self):9        # 创建标题10        title = Text("确界原理演示", font="STSong", font_size=48)11        12        self.play(Write(title))13        self.wait(1)14        self.play(FadeOut(title))15 16        # 创建坐标系17        axes = Axes(18            x_range=[0, 10, 1],19            y_range=[-1, 3, 0.5],20            axis_config={"include_tip": True},21            x_length=10,22            y_length=623        )24        25        x_label = axes.get_x_axis_label("n")26        y_label = axes.get_y_axis_label("x_n")27        28        self.play(Create(axes), Write(x_label), Write(y_label))29 30        # 创建一个有界但不单调的数列31        def sequence_func(x):32            return 2 + np.sin(x) * np.exp(-x/5)33 34        # 创建数列点和连线35        x_vals = np.linspace(0, 10, 50)36        points = [axes.coords_to_point(x, sequence_func(x)) for x in x_vals]37        curve = VMobject()38        curve.set_points_smoothly(points)39        curve.set_color(BLUE)40        41        dots = VGroup(*[Dot(point) for point in points[::5]])42 43        self.play(Create(curve), Create(dots))44        45        # 创建上确界线46        sup_value = 347        sup_line = DashedLine(48            axes.coords_to_point(0, sup_value),49            axes.coords_to_point(10, sup_value),50            color=RED51        )52        sup_label = MathTex(r"\sup x_n", color=RED).next_to(sup_line, RIGHT)53        54        # 创建下确界线55        inf_value = 156        inf_line = DashedLine(57            axes.coords_to_point(0, inf_value),58            axes.coords_to_point(10, inf_value),59            color=GREEN60        )61        inf_label = MathTex(r"\inf x_n", color=GREEN).next_to(inf_line, RIGHT)62 63        # 显示确界64        self.play(65            Create(sup_line),66            Write(sup_label)67        )68        self.play(69            Create(inf_line),70            Write(inf_label)71        )72 73        # 添加定义说明74        sup_def = Text(75            "上确界：数列的最小上界",76            font="STSong",77            color=RED78        ).scale(0.4)79        inf_def = Text(80            "下确界：数列的最大下界",81            font="STSong",82            color=GREEN83        ).scale(0.4)84        85        definitions = VGroup(sup_def, inf_def).arrange(DOWN, aligned_edge=LEFT)86        definitions.to_corner(UL)87        88        self.play(Write(definitions))89        90        # 演示上界性质91        epsilon = 0.292        point_above = Dot(axes.coords_to_point(5, sup_value + epsilon), color=RED)93        cross = Cross(point_above, color=RED)94        95        self.play(Create(point_above))96        self.play(Create(cross))97        self.wait(1)98        99        # 演示稠密性质100        for x in [2, 4, 6, 8]:101            point_near = Dot(102                axes.coords_to_point(x, sequence_func(x)),103                color=YELLOW104            )105            self.play(106                Create(point_near),107                FadeOut(point_near),108                run_time=0.5109            )110        111        self.wait(2)112 113def main():114    import os115    os.system("manim -pql supremum_infimum.py SupremumInfimum")116 117if __name__ == "__main__":118    main()