from matplotlib.pyplot import *
from mpl_toolkits.axes_grid.axislines import SubplotZero
from numpy import arange, sin, exp

x1 = arange(0.,9.1,.05)
x2 = arange(0.,9.6,.1)
z = lambda x: 3.*exp(-.4*x)
y = lambda x: sin(5.*x) * z(x)

fig = figure(figsize=(4,2))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)

ax.axis["top"].set_visible(False)
ax.axis["right"].set_visible(False)
ax.axis["left"].set_axisline_style("->")
ax.axis["bottom"].set_axisline_style("->")
ax.set_yticks([])
ax.set_xticks([])
ax.set_xlim(-1,10)
ax.set_ylim(-3,3)

ax.plot(x1,y(x1),'bo',ms=2.5)
ax.plot(x2, z(x2),'r--',lw=1.5)
ax.plot(x2,-z(x2),'r--',lw=1.5)

ax.text(10,-2.8,u'$n$')
ax.text(-.75,3,u'$X_n$')
fig.savefig("Cauchy_sequence_illustration.svg",bbox_inches="tight",pad_inches=.15)