我试图在乳胶中重现以下图像作为 Bolzano-Weierstrass 定理证明过程中的插图，但我无法做到。我真的不知道如何绘制点并标记所有内容，以便它看起来很棒，如下图所示：
我曾尝试使用 tikz 和 pgfplots，但我对它们都不够熟悉，无法获得我想要的结果。
谢谢您的帮助。
答案1
结果与 Sebastiano 的答案类似，但它没有使用绘图工具，而是使用图表。这样做的理由是，如果你有一个实际的系列，你也可以用类似的东西来绘制它
\draw[only marks,mark=*]
plot[samples at={1,...,15}] ({-1+5*(1+5*pow(-1,\x)/(2+\x))/\x},0);
完整代码：
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{decorations.pathreplacing,calligraphy}
\begin{document}
\begin{tikzpicture}[decoration={calligraphic brace, amplitude=6pt}]
\draw (-6,0) -- (6,0) (0,0.2) -- (0,-0.2) node[below]{$0$}
foreach \X in {-,} {(\X5.5,0.2) -- (\X5.5,-0.2) node[below] {$\X M$}} ;
\draw[only marks,mark=*]
plot[samples at={1,...,15}] ({-1+5*(1+5*pow(-1,\x)/(2+\x))/\x},0)
plot[samples at={1,...,5}] ({-\x},0);
\draw[decorate,thick] (-5.5,0.4) -- node[above=1ex](I1){$I_1$} (0,0.4);
\draw[decorate,thick] (0,-0.8) -- node[below=1ex]{$I_2$} (I1|-0,-0.8);
\draw[latex-] (-4,-0.1) --++ (0,-1) node[below]{$a_{n_1}$};
\draw[latex-] (-1,0.1) --++ (0,1) node[above]{$a_{n_2}$};
\end{tikzpicture}
\end{document}
答案2
这只是使用 Mathcha 创建的抽奖（https://www.mathcha.io/editor)，我非常喜欢。如您所见，此工具无法创建完美的绘图或非常短的代码。对于想要创建简单图像的用户，如果您需要快速获得代码，此工具可以作为帮助。显然，我邀请您阅读手册TikZ及其命令，以创建比我附加的更漂亮的绘图。这只是您图像的一个想法。
%% Compile and read me!
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,tikz}
\begin{document}
\tikzset{every picture/.style={line width=0.75pt}} %set default line width to 0.75pt
\begin{tikzpicture}[x=0.75pt,y=0.75pt,yscale=-1,xscale=1]
%uncomment if require: \path (0,300); %set diagram left start at 0, and has height of 300
%Straight Lines [id:da9924624130587041]
\draw (112.33,111.33) -- (519.67,110) ;
%Straight Lines [id:da8964467018788844]
\draw (130.67,101.67) -- (130.67,117.67) ;
%Straight Lines [id:da11386151785300402]
\draw (270.67,102.33) -- (270.67,118.33) ;
%Straight Lines [id:da13122160840712382]
\draw (375.67,102) -- (375.67,118) ;
%Straight Lines [id:da3445450640481962]
\draw (491,102) -- (491,118) ;
%Shape: Brace [id:dp6200800570089593]
\draw (375.5,97) .. controls (375.5,92.33) and (373.17,90) .. (368.5,90) -- (265.09,90) .. controls (258.42,90) and (255.09,87.67) .. (255.09,83) .. controls (255.09,87.67) and (251.76,90) .. (245.09,90)(248.09,90) -- (138.5,90) .. controls (133.83,90) and (131.5,92.33) .. (131.5,97) ;
%Shape: Circle [id:dp6841067146425215]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (147.33,110) .. controls (147.33,107.97) and (148.97,106.33) .. (151,106.33) .. controls (153.03,106.33) and (154.67,107.97) .. (154.67,110) .. controls (154.67,112.03) and (153.03,113.67) .. (151,113.67) .. controls (148.97,113.67) and (147.33,112.03) .. (147.33,110) -- cycle ;
%Shape: Circle [id:dp6659880770508297]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (177.33,110.33) .. controls (177.33,108.31) and (178.97,106.67) .. (181,106.67) .. controls (183.03,106.67) and (184.67,108.31) .. (184.67,110.33) .. controls (184.67,112.36) and (183.03,114) .. (181,114) .. controls (178.97,114) and (177.33,112.36) .. (177.33,110.33) -- cycle ;
%Shape: Circle [id:dp9504700751081823]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (206.67,110.33) .. controls (206.67,108.31) and (208.31,106.67) .. (210.33,106.67) .. controls (212.36,106.67) and (214,108.31) .. (214,110.33) .. controls (214,112.36) and (212.36,114) .. (210.33,114) .. controls (208.31,114) and (206.67,112.36) .. (206.67,110.33) -- cycle ;
%Shape: Circle [id:dp09029872211584267]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (236.67,110.33) .. controls (236.67,108.31) and (238.31,106.67) .. (240.33,106.67) .. controls (242.36,106.67) and (244,108.31) .. (244,110.33) .. controls (244,112.36) and (242.36,114) .. (240.33,114) .. controls (238.31,114) and (236.67,112.36) .. (236.67,110.33) -- cycle ;
%Shape: Circle [id:dp8167826233391373]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (386.67,109.67) .. controls (386.67,107.64) and (388.31,106) .. (390.33,106) .. controls (392.36,106) and (394,107.64) .. (394,109.67) .. controls (394,111.69) and (392.36,113.33) .. (390.33,113.33) .. controls (388.31,113.33) and (386.67,111.69) .. (386.67,109.67) -- cycle ;
%Shape: Circle [id:dp8722255959836276]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (427.33,109.67) .. controls (427.33,107.64) and (428.97,106) .. (431,106) .. controls (433.03,106) and (434.67,107.64) .. (434.67,109.67) .. controls (434.67,111.69) and (433.03,113.33) .. (431,113.33) .. controls (428.97,113.33) and (427.33,111.69) .. (427.33,109.67) -- cycle ;
%Shape: Circle [id:dp3361929558883294]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (447.33,109.67) .. controls (447.33,107.64) and (448.97,106) .. (451,106) .. controls (453.03,106) and (454.67,107.64) .. (454.67,109.67) .. controls (454.67,111.69) and (453.03,113.33) .. (451,113.33) .. controls (448.97,113.33) and (447.33,111.69) .. (447.33,109.67) -- cycle ;
%Shape: Circle [id:dp28390041233762386]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (474,109.67) .. controls (474,107.64) and (475.64,106) .. (477.67,106) .. controls (479.69,106) and (481.33,107.64) .. (481.33,109.67) .. controls (481.33,111.69) and (479.69,113.33) .. (477.67,113.33) .. controls (475.64,113.33) and (474,111.69) .. (474,109.67) -- cycle ;
%Shape: Circle [id:dp9615854303539904]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (279.33,111) .. controls (279.33,108.97) and (280.97,107.33) .. (283,107.33) .. controls (285.03,107.33) and (286.67,108.97) .. (286.67,111) .. controls (286.67,113.03) and (285.03,114.67) .. (283,114.67) .. controls (280.97,114.67) and (279.33,113.03) .. (279.33,111) -- cycle ;
%Shape: Circle [id:dp20494776974825157]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (312.33,110.67) .. controls (312.33,108.64) and (313.97,107) .. (316,107) .. controls (318.03,107) and (319.67,108.64) .. (319.67,110.67) .. controls (319.67,112.69) and (318.03,114.33) .. (316,114.33) .. controls (313.97,114.33) and (312.33,112.69) .. (312.33,110.67) -- cycle ;
%Shape: Circle [id:dp5303366846344186]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (321.67,110.67) .. controls (321.67,108.64) and (323.31,107) .. (325.33,107) .. controls (327.36,107) and (329,108.64) .. (329,110.67) .. controls (329,112.69) and (327.36,114.33) .. (325.33,114.33) .. controls (323.31,114.33) and (321.67,112.69) .. (321.67,110.67) -- cycle ;
%Shape: Circle [id:dp24820017851669074]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (330,110.33) .. controls (330,108.31) and (331.64,106.67) .. (333.67,106.67) .. controls (335.69,106.67) and (337.33,108.31) .. (337.33,110.33) .. controls (337.33,112.36) and (335.69,114) .. (333.67,114) .. controls (331.64,114) and (330,112.36) .. (330,110.33) -- cycle ;
%Shape: Circle [id:dp7653236409981055]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (303.33,110.67) .. controls (303.33,108.64) and (304.97,107) .. (307,107) .. controls (309.03,107) and (310.67,108.64) .. (310.67,110.67) .. controls (310.67,112.69) and (309.03,114.33) .. (307,114.33) .. controls (304.97,114.33) and (303.33,112.69) .. (303.33,110.67) -- cycle ;
%Shape: Circle [id:dp36351648225964683]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (344.33,110.67) .. controls (344.33,108.64) and (345.97,107) .. (348,107) .. controls (350.03,107) and (351.67,108.64) .. (351.67,110.67) .. controls (351.67,112.69) and (350.03,114.33) .. (348,114.33) .. controls (345.97,114.33) and (344.33,112.69) .. (344.33,110.67) -- cycle ;
%Shape: Circle [id:dp294024717030013]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (351.67,110.67) .. controls (351.67,108.64) and (353.31,107) .. (355.33,107) .. controls (357.36,107) and (359,108.64) .. (359,110.67) .. controls (359,112.69) and (357.36,114.33) .. (355.33,114.33) .. controls (353.31,114.33) and (351.67,112.69) .. (351.67,110.67) -- cycle ;
%Straight Lines [id:da6272191786740566]
\draw (210.67,159.67) -- (210.67,120.67) ;
\draw [shift={(210.67,117.67)}, rotate = 450] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle ;
%Shape: Brace [id:dp24141832145418474]
\draw (270.67,120.33) .. controls (270.7,125) and (273.04,127.32) .. (277.71,127.29) -- (313.38,127.07) .. controls (320.05,127.02) and (323.39,129.33) .. (323.42,134) .. controls (323.39,129.33) and (326.71,126.98) .. (333.38,126.94)(330.38,126.96) -- (369.04,126.72) .. controls (373.71,126.69) and (376.03,124.34) .. (376,119.67) ;
%Shape: Circle [id:dp2950234401571059]
\draw [fill={rgb, 255:red, 0; green, 0; blue, 0 } ,fill opacity=1 ] (359,110.67) .. controls (359,108.64) and (360.64,107) .. (362.67,107) .. controls (364.69,107) and (366.33,108.64) .. (366.33,110.67) .. controls (366.33,112.69) and (364.69,114.33) .. (362.67,114.33) .. controls (360.64,114.33) and (359,112.69) .. (359,110.67) -- cycle ;
%Straight Lines [id:da5496324871117824]
\draw (334,61.67) -- (334,100) ;
\draw [shift={(334,103)}, rotate = 270] [fill={rgb, 255:red, 0; green, 0; blue, 0 } ][line width=0.08] [draw opacity=0] (8.93,-4.29) -- (0,0) -- (8.93,4.29) -- cycle ;
% Text Node
\draw (126,126.67) node {$-M$};
% Text Node
\draw (378,132) node {$0$};
% Text Node
\draw (488.67,124.67) node {$M$};
% Text Node
\draw (256,75) node {$\scriptstyle I_{1}$};
% Text Node
\draw (210.67,168.67) node {$\scriptstyle a_{n_1}$};
% Text Node
\draw (325.33,142) node {$\scriptstyle I_{2}$};
% Text Node
\draw (344.67,55.33) node {$\scriptstyle a_{n_2}$};
\end{tikzpicture}
\end{document}