import matplotlib.pyplot as plt
import math


stirling = lambda n: math.sqrt(2 * math.pi * n) * (n/math.e) ** n
br = 5

x = [_ for _ in range(br)]
y = [math.factorial(_) for _ in range(br)]

x1 = [_ for _ in range(br)]
y1 = [stirling(_) for _ in range(br)]

plt.plot(x, y, label="factorial")
plt.plot(x1, y1, label="Stirling's approximation")
plt.legend()

plt.title("Stirling's approximation accuracy")
plt.xlabel("x")
plt.ylabel("y")
plt.show()