% draw an illustration of a sequence that is not Cauchyfunction main() % prepare the screen and define some parameters      figure(1); clf; hold on; axis equal; axis off;   fontsize=30; thick_line=3; thin_line=2;   black=[0, 0, 0]; red=[1, 0, 0]; blue=[0, 0, 1];   arrowsize=0.5; arrow_type=1; arrow_angle=30; % (angle in degrees)   circrad=0.07; % radius of ball showing up in places   B=9;   X=0:0.06:B;   f=inline('(X+2)./(X+0.8)', 'X');   Y=sin(5*X).*f(X);   for i=1:length(X)  ball(X(i), Y(i), circrad, blue);   end   X=0:0.05:(B+0.3);   Z=f(X);   plot(X, Z, 'r--', 'linewidth', thin_line)   plot(X, -Z, 'r--', 'linewidth', thin_line)   % draw the coordinate axes   shift=-3;   Kx=1.1; Ky=1.3;    L=max(Y);    arrow([-1 shift], [Kx*B, shift],  thin_line, arrowsize, arrow_angle, arrow_type, black)    arrow([-1, shift], [-1, Ky*L],    thin_line, arrowsize, arrow_angle, arrow_type, black)    text(Kx*B+0.6, shift,  '\it{n}', 'fontsize', fontsize, 'HorizontalAlignment', 'c')   text(-1, Ky*L+0.8,  '\it{x_n}', 'fontsize', fontsize, 'HorizontalAlignment', 'c')   % save to disk   saveas(gcf, 'Cauchy_sequence_illustration2.eps', 'psc2') % export to epsfunction ball(x, y, r, color)   Theta=0:0.1:2*pi;   X=r*cos(Theta)+x;   Y=r*sin(Theta)+y;   H=fill(X, Y, color);   set(H, 'EdgeColor', 'none');function arrow(start, stop, th, arrow_size, sharpness, arrow_type, color)   % Function arguments:% start, stop:  start and end coordinates of arrow, vectors of size 2% th:           thickness of arrow stick% arrow_size:   the size of the two sides of the angle in this picture ->% sharpness:    angle between the arrow stick and arrow side, in degrees% arrow_type:   1 for filled arrow, otherwise the arrow will be just two segments% color:        arrow color, a vector of length three with values in [0, 1]   % convert to complex numbers   i=sqrt(-1);   start=start(1)+i*start(2); stop=stop(1)+i*stop(2);   rotate_angle=exp(i*pi*sharpness/180);% points making up the arrow tip (besides the "stop" point)   point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);   point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);   if arrow_type==1 % filled arrow% plot the stick, but not till the end, looks bad      t=0.5*arrow_size*cos(pi*sharpness/180)/abs(stop-start); stop1=t*start+(1-t)*stop;      plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', th, 'Color', color);% fill the arrow      H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);      set(H, 'EdgeColor', 'none')         else % two-segment arrow      plot(real([start, stop]), imag([start, stop]),   'LineWidth', th, 'Color', color);       plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', th, 'Color', color);      plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', th, 'Color', color);   end